function and relation

 In the previous post we have discussed about Define one to one correspondence and In today's session we are going to discuss about function and relation.
Function and relation are two different concepts of mathematics. A relation is resembles a function only if it is one – one & onto. Therefore, we can say that all functions are relations but not all relations can be functions. In the Cartesian system we represent the 1^st value of ordered pairs as the x – coordinate and the 2^nd value as the y – coordinate. So, we can define a relation a usual set of orderly pairs and the mapping is not necessarily be one – one & onto.
Suppose we have two sets A = 2, 4, 5, 6, 8, 10 and B = 4, 16, 8, 10, 12. The mapping is done from set A to set B such that the elements in set B consist of multiples in set A. Element 4 of set B has multiples as 2 & 4 in set A. Similarly, for 16 we have 2, 4 & 8, for 8 we have 2, 4 & 8, for 10 we have 2, 5 & 10 and for 12 we have 2, 4 and 6. Thus this mapping is one to many mapping and thus this relation does not represent a function. Thus the ordered pairs we form are: (2, 4), (4, 4), (2, 16), (4, 16), (8, 16), (2, 8), (4, 8), (8, 8), (2, 10), (5, 10), (10, 10), (2, 12), (6, 12) and (4, 14).
To define a functionhttp://en.wikipedia.org/wiki/Function_(mathematics) we must have unique output for every input i.e. one value in range for every value in domain and also all the values of domain and range must be covered. For instance, we have pairs like: (1, 2), (4, 8), (2, 4), (3, 6) and (5, 10).
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Define one to one correspondence

 In the previous post we have discussed about What is Mathematical Induction and In today's session we are going to discuss about Define one to one correspondence.


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One to one correspondence can be defined as property of a set according to which every member of set is related exactly one member of another set. This concept is applied on sets. Set is just a way to store similar kind of values into it and describe the relationship between these values or objects. If we want to describe this concept in the form of simple definition then we can say that it is a situation which occurs only when members of one set are evenly matched with members of another set. According to this one to one correspondence; we need to remember one thing that any member of first set can make a pair with any one member of another set.

Suppose we have two sets which are named as A and B respectively. Set A and B has some members that are shown below:

A = a, b, c, d, e,

B = I, j, k, l, m,

If we follow one to one correspondence concept on above given sets then each and every member of set 'A' can make a pair with one member of Set 'B'.

A → B = a, i, b, j, c, k, d, l, e, m

Above each member of set A makes pair with only one member of Set B. Any member of Set A can make pair with any member of Set B, there is no restrictions to make a pair. One more thing we need to remember is that none of the member should be left as unpaired. It means each and every member must carry a pair value with another set.

In mathematics, concept of Molality Formula can be denoted by numbers of moles of any given substance per liter of solution.

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What is Mathematical Induction

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Mathematical Induction is basically a technique which is used to establish the proof that a given statement is true for all positive integers or natural numbers. We need to prove two statements which are: First statement in the infinite sequence of statements should be true and if anyone statement in infinite sequence of statements is true then next statement will also be true.

Suppose, we have 'n' natural numbers then P(n) holds all natural numbers so:

0 + 1 + 2 + 3 + 4 + 5 +.........+ n = n (n + 1) / 2,

Where P(n) provides a formula to calculate the sum of natural numbers.

Now we use inductive step to prove the above statement. Where P(k) holds natural number then according to statement P (k + 1) also holds then

(0 + 1+ 2+...................+ k) + (k + 1) = [(k+ 1) ((k+ 1) + 1)] / 2,

After using the induction hypothesis:

k (k + 1)/ 2 + (k + 1),

k (k + 1)/ 2 + (k + 1) = [k(k + 1) + 2(k + 1)] / 2,

= (k² + k + 2k + 2) / 2,

= (k + 1) ( k + 2) / 2,

= [(k + 1) ((k + 1) + 1)] / 2.

So the resulting equation shows that P (k+ 1) also holds.

To understand it, we will take an example: We have an equation 23ⁿ – 1 and we have to prove that it is divisible by 11 for all positive integers 'n'.

So, to prove that we put the value of n = 1 then

23¹ – 1 = 22 which is divisible by 11.

Now, according to induction theorem if P (k) holds then P (k + 1) also holds so

23^{k + 1} – 1= 23. 23^k - 1

= 11. 2. 23^k + (23^k – 1),

Here we can see that resulting equation is divisible by 11.

Multiplying and Dividing Fractions is a concept of algebra.

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word problem help

In the previous post we have discussed about Relations and Functions and In today's session we are going to discuss about word problem help. The study of mathematics is basically aimed with relating it with the real life so that the objective of studying math is fulfilled.  Our life basically related to math at every angle of life.
By word problems we mean that the statements of the problems are given from the real life and we need to get the solution to the problem by understanding the mathematical operation to be performed.  To get word problem help, we can visit online math tutors which can support us to learn the logics to be used in solving the word problems.
We need to master the concept of analyzing the type of the problem and then check which mathematical operation will be performed on the given problem in order to get the solution. We are given certain tips to find the key words which help us to check the operation to be performed. Suppose we have the key words like add, sum, join, combined, greater, in all etc. we simply conclude that the sum of the digits will  help us to get the solution of the problem. In the same way if we have the words like less, reduce, decreased by etc help us to get the solution  for the given problem.

Students can take online help to  learn how to perform the operations of maths and solve the word problems. Different practice worksheets are also available online which help to develop the confidence. They help us to practice variety of word problems and get the real exposure to a variety of problems.
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Relations and Functions

In the previous post we have discussed about Rotation Matrix and In today's session we are going to discuss about Relations and Functions. In mathematics, there are various ways are described that can maintain data in records in quick and accessible manner. Regarding to these technology relation and function are one of them. A Relations and Functions are two different things but they together to perform any particular task. A relation can be describing as a relationship between sets of data or values. Suppose there is a class in school. There are thirty students in class and each student has their own marks in particular subject. Now make a pair between names of students and their marks are known as relation.
On other hand arrange a pair of data in particular order can be considering as function. In the simple mean we can define the concept of Relations and Functions by using the concept of ordered pair which carries two values into it. Now on the basis of ordered pair a relation can simply be define as set of ordered pairs of values Like ( a0, b). Here ( a, b) can be consider as a ordered pair where value of ‘a’ can be considered as a value of domain and the second value of ordered pair are known as range. Here two new concepts arise during discussion that is domain and other is range. Here domain is known as collection of all first value of pair and range can be defined as collection of second value of ordered pair.
By using the definition of range and domain we can say that function is a process where the domain value makes a pair with only one value of their range. In mathematics, the values of ordered pair can either be negative or positive.
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Rotation Matrix

Hi friends, in mathematics, today we will discuss about Rotation Matrix. And also we will study different method to solve the rotation matrix. Generally a rotation matrix is used to show a rotation in linear algebra. For example:

p = [ cos Ф - sin Ф]

      [ sin Ф cos Ф]

In the matrix mention above matrix points are rotated in xy – Cartesian plane ( here x is along to horizontal axis and y is along to vertical axis) through an angle Ф about the origin of coordinate system. Using the matrix multiplication we also found a rotated vector. So there is no effect of multiplication on zero vector or in other word it can be a coordinates of the origin. Commonly rotation matrix is used to calculate rotations about the origin of coordinate system. It can also be used to assist a simple algebraic description of such types of rotations and it can also be used for computation in physics, geometric, etc. If we talk about the case of three dimensional space then the rotation can be stop by given angle along a single axis of rotation. So, it can be simply calculated by an angle and vector by three entries. In case of 3x3 Rotation Matrix. It can be solved by nine entries of a rotation matrix that has three rows and three columns. It can not be used in higher dimensions. (know more about Rotation Matrix, here)

It is also said to be orthogonal matrices that has determinant value is equal to 1. It can be denoted as:

= Pa = P-1, det P = 1. this type of matrices are called as special orthogonal group. It can be denoted as 'SO (n). Entire rotational matrices are found using these matrix multiplication. For example:

= Pp (γ) Pq (β) Pr (α); it can be denoted as a rotation whose angles are α, β, γ. This is all about rotation Matrix.

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Binary Numbers

In the previous post we have discussed about domain math and In today's session we are going to discuss about Binary Numbers. Before discussion about the Binary Numbers first we have to know about the number system that is a basic need for presenting a number. When we talk about any number it consist some of the digits in it and these digits is decided by the number system which is used to express the number. So there are basically four types of number system as decimal , binary , octal and hexadecimal number system . When we talk about the binary number system in which binary means two , so there are only two digits for expressing a number that are zero (0) and one (1). (know more about Binary Numbers, here)
In binary number system, all the values having two digits. When we talk about any number probably it is define into the decimal number system in which number having the value from 0 to 9 and all these 10 digits are used  to make different types of number and when we want to change any decimal number into the binary number that means every single digits of the given number will be multiplied with the  exponent of two that means if there is a number xyz and we want to change it in the binary number then in x y z ,digit x has a hundred position , y has a tens position and z has a ones position and then z is multiplied with the  2 >0 and y multiplied with the 2 > 1 and x is multiplied with the 2 > 2.
 Temperature Conversion Chart is used for define the temperature in different units and also describe the relation between these units that is used for changing the temperature in one unit to another.
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domain math

In mathematics, function is used to show the relationship between values. Each input values of a function gives back exactly one output value. Now we will see how to find the domain math? Suppose that we have a function and we want to find the domain of a function then first it is necessary to know about the definition of domain in function.

If we select the entire ‘x’ coordinate values of a function, all the x – coordinate values are said to be domain of a function. In the same way, the possible ‘y’ coordinate values are said to be range of a function.

Suppose we have some values (8, -15), (-10, 1), (16, -5), (-2, 6), then the domain of function is all the ‘x’ coordinate values. (know more about domain math, here)

Domain = 8, -10, 16, 6.

Range is all ‘y’ coordinate values,

Range = -15, -10, 16, 6.

let's see some steps to find domain of a function.

To finding the domain of a function we follow some steps:

Step1: To find the domain of a function first we have to assume a function which contains ‘x’ and ‘y’ coordinates.

Step2: As we know the domain of a function is all ‘x’ coordinates values.

Step3: In a function if we have values of ‘x’ and ‘y’ coordinates then we can easily find the domain and range of a function.

If we follow these steps then we can easily find the domain of a given function. This is how we can find the domain of a function. Now we will see Taylor Series Expansion. Taylor series can be defined as a series of a function about a function. It is generally used in the approximation of a function. To get more information about Taylor series then follow online tutorial of icse syllabus. In the next session we will discuss about Binary Numbers. 

Translation Math

In the previous post we have discussed about Symbolic Logic and In today's session we are going to discuss about Translation Math. In mathematics, to move a figure or a shape from one place to another we use translation. In this a figure in a plane can be move upward and downward, right, left or anywhere. It is a function that moves every point a constant distance in a particular direction. Suppose we move one point of a shape like Triangle, Square, Line, etc up to five unit in a particular direction by translation, then all the points will move by five unit in same direction. Thus only the position of the object changes but its size remains the same.

To understand better let us translate in the following graph:

The graph on the left side is translated to the graph on the right side.

The equation of the absolute value function of left hand side graph:

y = |x|.

When the function f(x) is translated ‘p’ units horizontally, then the argument of f(x) becomes x − p.

Thus as the origin is moved to (3, 4), the new equation by its translation is:

y − 4 = |x − 3|.

Let us have a rectangular on a graph with the points P(-4, 8), Q(1, 8), R(-4, 4), S(1, 4). To shift it by four unit downward we use the following steps:

As the figure is being translated by “four” unit in downward direction, there will be no changes in x- coordinate. (know more about Translation Math, here)

1. subtract by 4 in y coordinate, we get

P(-4, 8) after translation (x - 0, y – 4),

=> (-4 - 0, 8 – 5),

• (-4, 3)

2. For Q(1, 8) after translation, we get (x - 0, y - 4)

• (1 - 0, 8 - 5)
• (1, 3) translated coordinate.

3. For R(-4, 4) so, after translation (x - 0, y - 4)

=> (-4 - 0, 4 - 4)

=> (-4, 0) translated coordinate.

4. For S(1, 4), after translation,we get (x - 0, y - 4)

=> (1 - 0, 4 - 4)

=>(1, 0) translated coordinate.

So, translated figure coordinates will be points P(-4, 3), Q(1, 3), R(-4, 0), S(1, 0).

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Symbolic Logic

Hi friends, in this blog we are discussing an important topic that is 'Symbolic Logic'. Symbolic Logic is a method that is used to distinguish logical expressions using symbols and variables, relatively than in ordinary language. Symbolic logic is used in removing the uncertainty. In mathematical field, so many systems of symbolic logic are mention below:
(1.) Classical propositional logic,
(2.) First-order logic,
(3.) Modal logic.
In mathematics, all the symbolic logic are divided by different symbols, or exclude the use of certain symbols. Let's see some of the symbolic logic symbols. Here we will see the basic logic symbols.
(1.) (┑): - This given symbol is known as negation.
Explanation: Let we have a statement ┑A that is true if and only if the value of 'A' is given as false.
= ┑ (┑A) ⇔ A.
(2.) (∨): - This given symbol is known as logical disjunction.
Explanation: The statement A ∨ B is true if and only if the value of 'A' and 'B' both are true, or if both are false.
(3.) (⊕): - This symbol is known as exclusive disjunction.
Explanation: let we have a given statement A ⊕ B then the condition is true if value of 'A' and
'B' are true but not both the value true.
(4.) (T): - This symbol is known as Tautology.
Explanation: Here the meaning of this symbol is A ⇒ B is always true.
(5.) (∃): - This symbol is known as existential quantification.
Explanation: let we have a given statement ∃ x A (x), it means there is at least one x such that A (x) is true.
(6.) (∃!): - This symbol is known as uniqueness quantification.
Explanation: let we have a given statement ∃! x A (x), it means there is exactly one x such that A (x) is true. Solving Differential Equations is a part of trigonometry. It includes application of derivative. To get more information then we need to follow icse syllabus 2013. It helps so much for solving the differential equation.

How to Tackle Recursion

In the previous post we have discussed about How to Define Complements in Mathematics and In today's session we are going to discuss about how to Tackle Recursion. The term recursion is generally used in many subjects including the subject of the math. Many of us do not exactly know the meaning of this term in the context of the math. So in this article we will have a look on some of the important facts of the term recursion. (know more about Radical, here)

Now let us start with the definition of the term recursion. It is a method in which we repeat the items in a way which is self similar. It should be noticed that in a situation where the surfaces of any 2 mirrors are completely parallel to each other then the nested type of the images which we see can be said to be the form of an infinite type of the recursion. This term can give different types of the meanings especially to the varieties of the disciplines which range from the linguistics to the logic.
We will now discuss about some of the uses of the recursion. One of its very common uses in the field of the mathematics is the one where it is being referred to a process in which we define the functions where the function which is defined is being applied within the definition of its own.   
Particularly it can be used to define almost infinite no. of the instances that is the values of the function with the help of an expression which is finite which for some of the instances may be referred to other of the instances but in that way where any loop or a chain which is infinite cannot occur. However the term recursion is also utilized very commonly to explain any process of the objects which are repeating in a way which is self similar.
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How to Define Complements in Mathematics

In the previous post we have discussed about How to Read Binary and In today's session we are going to discuss about Complements, the word Complements can be refered as a concept that perform there different task in various field of mathematics. In a simple mean we can say that complement is a amount which can be added to something of same kind to generate its whole. The definition of Complement varies according to the different fields of mathematics.
In the geometrical mathematics the word Complements can be express as angle of 90 degree which is formed by adding two different angles. In geometry, one angle said to be complement for the other angle to make a whole angle. Suppose the measure of one angle is 35 degree and the measure of other is 55 degree then merge up of these angles form a 90 degree angle that can be consider as a whole angle.
In the same aspect of set theory, the word  Complements can be define as a inverse of any set. As we know that a set is a collection of elements that are also exists in universal set. In the same aspect the concept of complement for a set S can be define as a set of all elements that are not exists in the set A. Suppose there is a set B, so the Complements of B contains all the elements that are exists in universal set U but do not contain by set B. In the mathematical notation complement of set can be express as below given format:
Complement of B = (B)'
Suppose the set B = (1, 2, 3 ) And Universal set U contains (a, b, c, 1, 2, 3) then 
Complements of set B can be represented as in below given format:
B' = (a, b, c)
when we add both set then it make whole set which can be called as universal set. It means to say that set B + Set B' = U set.
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How to Read Binary

In the previous post we have discussed about How Online Matrix Calculator and In today's session we are going to discuss about How to Read Binary. Decimal Numbers are the numbers which include 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 . We do all our mathematical processing in the form of decimal numbers. Binary numbers are the numbers which can be expressed in the form of 1 and 0 only. The data stored in the computers, calculators, chip is all in the form of digits and so it is in the form of binary codes.  These Binary numbers can be converted in the form of decimal numbers. Here we are going to learn about How To Read Binary.
Let us take the example of the binary number say 1 0 0 1. To convert the given binary number, we will start reading the data from the right hand side and place the numbers with base 2 and power 0 at the first place. The power goes on increasing by 1as we move from right to the left. SO the first digit will be 2 >0 = 1, followed by 2 >1 = 2, then we proceed as follows:
2>2 = 2 * 2 = 4
2>3 = 2 * 2 * 2  = 8
2> 4 = 2 * 2* 2 * 2  = 16
Thus the series appears as follows: 1, 2, 4, 8, 16 , 32 . . . .. .. which will be written along with the binary digits starting by right as follows
 8      4        2       1
1       0        0       1
Now we write 1 * 8 +  4 * 0 + 2 * 0 + 1 *1 = 8 + 0 + 0 + 1 = 9, which is the decimal number. (know more about Binary, here)


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How Online Matrix Calculator

In the previous post we have discussed about How to Understand Functions and In today's session we are going to discuss about How Online Matrix Calculator. In this blog we are going to discuss about the on line matrix calculator that is an on line tool for calculation on the given matrix. It is solved the desired operation on the given matrix in very less period of time .For using this tool user only enter the desired matrix into the text box and there are values are separated by the spaces or comma. Calculator calculates all the operations that are specifies in the text box and also give the accurate answer efficiently. There are concepts of calculating the operations on matrix's are different from the general type of operations as addition, subtraction, multiplication or division. (know more about Matrix , here)
There are several operations that are done on the matrix as addition, subtraction, multiplication or division. There are some other operations as inverse of matrix or transposition of matrix are also done by the on line matrix calculator.
 If we have two matrixes a [] and b [] then according to the different operation we can show it as follows:
[ a11 a12 [b11 b12 [ C11 C12
a21 a22 ] <operator> b21 b22] = C21 C22 ]
These matrixes are entered to text box of the on line calculator and select the desired operation that will perform by the calculator and it automatically generates the answer in form of another matrix.
There are also some of the complex calculations that are defined as Matrix Transpose, MatrixInverse done by the online matrix calculator. In some advance online matrix calculator some of the calculations as QR Decomposition and Moore – Pen-rose Inverse and LU Decomposition and Matrix Trace are also performed.
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How to Understand Functions

In the previous post we have discussed about What are Binary Numbers and In today's session we are going to discuss about How to Understand Functions. The concept of functions is of paramount importance in mathematics and among other disciplines as well. Functions are the relation between the set of inputs and the set of possible outputs that a follow a property i. e. each input is associated definitely with one output. (know more about Function, here)
A function 'f' from a set P to a set Q associates each element of set P to a unique element of set Q.
Terms such as “map” (or “mapping”) correspondence used as synonyms for “function”. If f is a function from a set P to a set Q, then we write f: P → Q or P → Q, which is read as f is a function from P to Q or f maps P to Q.
We use some standard real function such as constant, identity, modulus, greatest integer, smallest integer function and many more. We can also perform many operations on the above function like addition, product, subtraction, quotient etc.
There are some types of function are defined in calculus.

I.            One -one function: - It is also known as injection function. If different items of P have different images in Q, then it is said to be one-one function.

II.            Many-one function:- If two or more items of a set P have the same image In Q, then it is said to be many-one function.

III.            Onto function: - It is also known as surjection function. If every element of Q is the F-image of some element of P, then it is said to be onto function.

IV.            One-one onto function: - It is also known as bijection function. If it is one-one as well as onto, then it is said to be one-one onto function.

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What are Binary Numbers

In the previous post we have discussed about binary subtraction and In today's session we are going to discuss about What are Binary Numbers. In mathematics, binary number plays a vital role in the study of number system. What are binary numbers? Many students ask this question. Binary number composed or involved of two number i.e. 0 and 1. There are many operations which are performed by the binary number such as addition, subtraction, multiplication and division. The state of 0 is off and 1 is on.
Binary numbers are basically used in logic gates, computers and many digital electronics circuits.
Let’s deal with the addition of binary number:
Addition of binary number is carried by two steps:

·         1+ 1 = 0 and the carry left goes to the other column.

·         1+ 0 = 1

Suppose we have to add two binary numbers:
Example:
   0 0 0 1 1 1 1 0
+ 1 1 1 0 0 0 1 0
 1 0 0 0 0 0 0 0 0
Here carry 1 goes to the next column.
Now, subtraction of binary number is given by:

·         1 – 0 = 1

·         1 – 1 = 0

·         0 – 0 = 0

·         0 – 1 = 1(with carry from the left side)

Suppose we have to subtract two number:
Example:
   1 1 0 1 (in decimal this is 13)
  -0 1 1 1 (in decimal this is 7)
   0 1 1 0  (so the resultant is 6 in decimal)
( in the first column from the right there is 1-1=0, in the second column 0-1=1 and 1 is carry from the left one, in third column there is 0 remaining in the place of 1 so it will also take carry from left one so the subtraction is 1and in the fourth column 0-0=0 so the total result is 0 1 1 0 ).
Some binary numbers are given below:
The code for binary number is A B C D
                                                8 4 2 1
1 = 0001
2 = 0010
3 =0011
And so on.
Binary numbers and significant figures calculator are well described in CBSE board.

binary subtraction

Now today we will discuss about binary subtraction. In the mathematics the number which has base two is known as binary number. In binary number system only two digits are used which are 0 and 1.
For example: 1011 represents (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰), they represent 8 + 0 + 2 + 1, and equals to 11.
Now we will see the binary subtraction.
To finding the subtraction in the binary number system we have to follow some of the step which is given below.
Step1: Calculating subtraction first we take the number.
Step2: It is necessary to remember that the number should be in the form of 0 and 1 binary digit.
Step3: Subtracting the values we have to follow such above conditions, if we subtract the number 0 from the number 0 then we get 0. When we subtract number 1 from the number 0 then we get 1. We subtract the number 0 from the number 1 then we get 1 with borrow. When we subtract the number 1 from the number 1 then we get 0, all these values have base 2 because the binary number is defined in the base 2 only.
Suppose we have 01010 and 1010, and we to do subtraction then it can be done as shown below.
For subtraction we need to follow above steps to find the result.
Step1: First take two numbers and the numbers should be in the form of binary number system.
01010 and 1010,
Step2: Then apply all the steps one by one.
(01010)₂ – (1010)₂
01010
  1010
If we subtract 0 from 0 then we get 0; rule number 1;
01010
  1010
        0
If we subtract 1 from 1 then we get 0; apply rule number 4;
01010
  1010
      00
now subtract 0 from 0 we get 1.
01010
  1010
    000
Now we subtract 1 from 1 then we get 0.
01010
  1010
  0000
Now borrow will add to next digit. So the number is:
01010
  1010
 10000
So the value is 10000.
Gamma Distribution is related to the statistical distribution which is also related to the beta distribution. ICSE examination is organised by the council for the Indian school certificate examination and in next session we will discuss about What are Binary Numbers.

one-to-one correspondence

In the previous post we have discussed about truth table and In today's session we are going to discuss about one-to-one correspondence, It is a condition when all the elements of one set say set ‘T’ is matched with the member of other set say set ‘R’ . The other name of the one-to-one correspondence is bijection and bijective function. Here none of the member of the set remains unpaired. It means each element of one set is paired with the other element of the other set. The one-to-one correspondence from set T to set R has the inverted function from set T to set R. also we can say this if set T and set R has the finite number of elements then the presence of one-to-one correspondence states that the sets pursue the same number of element. One-to-one correspondence from all the sets to all members of the set are sometime termed as permutation. One-to-one correspondence also has many applications in many areas of mathematics which include definitions of permutation group, projective map, homeomorphism, etc.
To do the perfect pairing with between the set T and set R one-to-one correspondence must follow four properties, they are:

•  Each element of the set ‘T’ must be paired with one of the element of set ‘R’.
• Not even a single member of set ‘T’ should be repeated to form the pair with other member of set ‘R’.
• Each element of set ‘R’ must be matched with at least one element of set ‘T’.
  • None of the member of set ‘R’ can be paired with the more than one element of set ‘

If the one to one correspondence satisfies the first two properties than it is surjective in nature and if it satisfies the last two properties than it is injective in nature, Hence we can conclude this the one-to-one correspondence is both surjective and injective in nature.

You can also study the topic place value worksheets. And this topic you can find in the CBSE class 10 sample papers.

truth table

A truth table is a table in mathematics used in logic especially in representation in Boolean algebra, it is also an alternate of truth table, It is used for the calculation of functional values on each expressions on their arguments. It simple words we can say that this table help us in checking whether an expression result is true for all the values we enter as input or it is logically valid
Representation of a truth table is where one column is for the input variable individually and one column for all the results of the operation for which this table is designed. The top row represents the variables from the expressions and various combinations
It is breaking of logic functions by identifying all the values the expression can have. It normally represents two input columns but can be increased up to any number according to the requirement of the problem. The values in input column are in the form of binary numbers
The three operations basic functions have are:
1. Not operation-It is also called as negation or inversion and is represented with symbol “-“
2. OR operation-It is called as addition or disjunction operation and is represented with symbol “+”
3. AND operation- It is called as multiplication or conjunction operation and is represented with symbol “*”
These functions are usually assigned the logic values 1 or 0 where 1 means true and 0 means false
Some Rules of the Truth Table are
If X = 0, then -X = 1
If X = 1, then -X = 0
X+Y = 1 except when X = 0 and Y = 0
X+Y = 0 if X = 0 and Y = 0
X*Y = 0 except when X = 1 and Y = 1
X*Y = 1 if X = 1 and Y = 1
For Diameter of a Circle and CBSE board sample papers for class 10 visit online educational portals and In the next session we will discuss about one-to-one correspondence.

free math problem solver with steps

We should know how to use the facility of Free Math Problem Solver with Steps, which guides us how to follow the steps for solving the math problems online. These problems can be based on different topics. In general a child of grade 6 has the problems based on profit and loss, percentage, simple interest and the compound interest and how to solve the mathematical expressions having more than one operation.  To solve the problems of mathematical expression, we have certain set of rules to be followed, which tells us which mathematical operation is to be performed and then which operator needs to be followed.  This is called the hierarchy of operations to be performed. In the hierarchy of operations, we will follow the rules of BODMAS, which means the following:
 B stands for Bracket
O – stands for Of operation
D- stands for division of terms
M- stands for  Multiplication of terms
A – stands for the  Addition Operation
S- Stands for the Subtraction operation.
 Thus we observe that if we follow this hierarchy of operation, it is clear that every time anyone will perform the operation of solving the expression, we say that the   result for the given expression will remain same. Thus  when the result for the expression is to be calculated, we ensure that first we will open the brackets and for this the operations in the brackets are to be  performed, followed by  “ of “ operation, then we perform division, then multiplication , then addition followed by subtraction operation.
 In order to learn how to use online Calculating Confidence Intervals, we must be aware of the free online features available on the above topics.  To know about the curriculum and the subject available in Ap State Board Of Secondary Education, a child should be able to understand the subject online.
In the next session we will discuss about De Morgans law and if anyone want to know about Lines of Symmetry Shapes then they can refer Internet and text books for understanding it more precisely.

online tutors homework help

To solve ,Algebraic Equations we will separate the constants and the variables and thus get the value of the variable in the given equation. In order to get the value of the variable, we need to  move the constant  on one side and the variables are moved to another side of the equation. Always remember that while we solve the equation, and we need to move a term from lone side of the equation to another, then the positive term will change to a negative term and a negative term will change to a positive term.  In the same way, we change the sign of multiplication to division and the relation of division changes to multiplication, thus the algebraic equations are solved and we get the value of the variable of the equation. To check that the value of the variable calculated is correct or not, we will place the value of the variable in the given equation and we find that the value satisfies the equation.
We must remember that a linear algebraic equation can have only one value or solution to the given equation. On the another hand a quadratic equation can have  at most two values of the variables,  and if the equation is a cubic equation, then we say that the variable can have  at the most three values. So we say that quadratic equations can have no solution, one solution or at the most two solutions. In the same way a cubic equation can have either 0 or 1, or 2 or 3 values of the variables.We have different ways to solve the equation and to get the solutions for the given linear equations.
We always have online tutors homework help to know and to learn more about Tamilnadu Board Logic Sample Papers.
In the next session we will discuss about free math problem solver with steps
and if anyone want to know about Axis of Symmetry then they can refer Internet and text books for understanding it more precisely.

Distributive law and prepositions

Hello students, Previously we have discussed about subtracting integers worksheet and In today's session we are going to discuss about Distributive law and prepositions which comes under state board of maharashtra syllabus, In mathematics we study many laws like distributive, idempotent, complement, and associative laws. In this session, we are going to discuss the Distributive Law and Prepositions which are generally used in various fields of mathematics. These laws come in Boolean Algebra laws and are basic laws of the algebra too for showing logical equivalence (i.e. a kind of relationship between the two expressions).
The Common Distributive Law can be stated for all real number x, y and z as:
x ( y + z ) = x y + x z
The statements x ( y + z ) define the order in which we will add the y and z values then multiply x by the result.
The statements x y + x z define the order in which we multiply x and y, then multiply x and z and then add the multiplied results.(Know more about Distributive law in broad manner, here,)
Just take an example to understand it: -
x = 4, y = 5, z = 6
The distributive law is x ( y + z ) = x y + x z
Solution: - 4 (5 + 6 ) = 4 . 5 + 4 . 6
Note :- ( . ) dot operator specifies the multiplication.
4 ( 11 ) = 20 + 24
44 = 44
The Distributive law in terms of logical equivalence (explained with the help of prepositions which can be defined as symbols that show mathematical relationship between two statements) is:-
P ∧ ( Q v R ) = ( P ∧ Q ) v ( P ∧ R )
P v ( Q ∧ R ) = ( P v Q ) ∧ ( P v R )
Where preposition ∧ is used for AND, and v for OR operation.
So these laws describes the two different ways but both ways produce same results.
In the next session we are going to discuss online tutors homework help
and if anyone want to know about Congruence and Similarity then they can refer  Internet and text books for understanding it more precisely.

De Morgans law

Previously we have discussed about multiplying polynomials worksheet and In today's session we are going to discuss about Law of De Morgans which is a part of maharashtra higher secondary board syllabus, It interchanges an equation form to its negation form. Here negation means its opposite form. The law provides some rules that are known as transformation rules because it transforms an equation form to its negation form. By De Morgans law, we can relate conjuction and disjunction in terms of each other.
In simple english, Applying negation on the conjuction form of an equation gives us the disjunction of its negations. In other words, Applying negation on a disjunction form of an equation gives us the conjuction of its negations.

In logical language form,De Morgans law can be expressed as,
( A á´§ B ) ' = ( A ) ' á´  ( B )'
( A á´  B ) ' = ( A ) ' á´§ ( B )'

here ' stands for the negation of the expression.
á´§ stands for the conjuction of two expressions.
á´  stands for disjunction of two expressions.
= sign stands for equality,i.e we can replace one form to another form
The law has many forms.i.e, we can define the law in many ways.

This law has the same meaning in set (Data Set Example) theory.

The substitution form of this law is as follows ,

X . Y = ( X' + Y ' )'
X + Y = ( X' . Y ')'
. stands for conjuction and + stand for Disjunction .
' stand for the negation .

This law also holds for the functional forms as,
if we have two functional operator X and Y, then

X AND Y = NOT ( ( NOT X ) OR ( NOT B )
X OR B = NOT ( ( NOT X ) AND ( NOT Y ) )

AND operator stands for the conjuction and OR operator stands for the disjunction .(Know more about De Morgans law in broad manner, here,)
NOT operator stands for the negation.
In the next session we are going to discuss Distributive law and prepositions
and Read more maths topics of different grades such as Geometric Shape Attributes in the upcoming sessions here.

Boolean Laws

Hi friends, Previously we have discussed about slope worksheets and today we are going to learn about Boolean Laws, one of the most interesting and a bit complicated topic of mathematical world named as Boolean Algebra that comes into maharashtra education board. To solve Boolean Algebra problems what we need to do is hard work and a daily little practice. Boolean laws and theorems are also needed to understand before starting to solve boolean algebra.
Boolean Algebra :-It was developed by George Boole in year 1840 , it represents logical calculus of truth values and algebra of real numbers with operations like ab , a+b ,
Boolean algebra (or Boolean logic) is a logical calculus of truth value, developed by George Boole in the 1840s. It resembles the algebra of real numbers, but with the numeric operations of multiplication xy, addition x + y, and negation −x replaced by the respective logical operations, (Know more about Boolean Laws in broad manner, here,)
It is algebra of two algebra values where one can be either true or false
Boolean Laws:

Identity for Single Variable
Operations with 1and 0: 1. A+ 0 = A (identity) 3. A + 1 = 1 (null element)	2. A.1 = A 4. A.0 = 0
Idempotency theorem: 5. Y + Y = Y	6. Y.Y = Y
Complementarity: 7. X + X’ = 1	8. X.X’ = 0
Involution theorem: 9. (Y’)’ = Y
Identities for multiple variables
Commutative law:  10. A + B = B + A	11. A.B = B.A
Associative law: 12. (X + Y) + Z = X + (Y + Z)      = X + Y + Z	13. (XY)Z = X(YZ)        = XYZ
Distributive law: 14. a(b + c) = ab + ac	15. a + (bc) = (a + b)(a + c) Example :  (A+B)(AC+AC)+AB+B Solution :(A+B)A(C+C)+AB+B (A+B)A+AB+B A((A+B)+B)+B A(A+B)+B AA+AB+B A+(A+T)B A+B

Conjunction disjunction and Complement are the three basic operations which we can perform on Boolean values.
In The Next Topic We Are Going To Discuss Boolean Laws and if anyone want to know about Constructing geometry shapes then they can refer to Internet and text books for understanding it more precisely.

Bi Conditional Statements

Previously we have discussed about number line worksheets and In today's session we are going to discuss about Bi conditional statements which is a part of maharashtra state board of secondary and higher secondary education ac provides you excellent college algebra help. They are used to write the definitions in the geometry. In geometry definition is defined as statements for defining the mathematical objects and these statements are written in the form of bi conditional statements. For creating the bi conditional statements we combine the conditional statements and also converse it .
Bi Conditional statements are the statements that are written in the form of “ x if and only if y; “ that have the meaning that if x is true then y is also true. Bi conditional statements “ x if and only if y “ is also write as “ x iff y “ or x < - > y .
When both the conditional statement and its converse are true then its bi conditional statement is also true . When both the conditional and its converse are false then the bi conditional statement is also false .
Bi conditional statement examples:
If there are two statements x : A polygon is a triangle .
Y : A polygon has absolutely 3 sides .
So the problem based on these statements is determine the truth values of these statements :
( x → y ) > ( y → x ) .This compound statement is defined as the conjunction of the two conditional statements .In these type of statements the first statement is known as hypothesis and statement y is known as the conclusion .In the second statement y is the hypothesis and x is the conclusion .

The above statements are described by the truth table as :
x    y  x->y   y->x   ( x → y ) > ( y → x )
T    T    T          T        T
T    F    F          T        F
F    T    T          F        F
F    F    T          T        T
When both the statements have the same truth values then the compound statement
( x → y ) > ( y → x ) is also true . So , this is the way of combine the two conditional statements and have a bi conditional . In the next topic we are going to discuss Boolean Laws and if anyone want to know about How to solve Perpendicular equations then they can refer to Internet and text books for understanding it more precisely.

Compound Statements

Previously we have discussed about math equation solver and Today I am going to discuss about the compound statements in discreet math( you can also try compound interest calculator) which is a part of maharashtra secondary and higher secondary education board. Compound Statements in mathematics is very interesting and easy to learn. As we know that compound means combining two or more parts as to form a mix, so here we will learn to make the compound statements and how to solve compound statements. To compose a compound statement there are various ways. For this we have many connectors such AND, OR, IF….THEN, NOT etc.

Instead of using a simple statement again and again we use a single letter which represent whole thing. For example: (want to Learn more about Compound Statements, click here),

Statement: “I have money.”
A : “I have money”.
 We can replace this statement by ‘A’. So we don’t need to use this statement again and again, instead of this we simply use ‘A’.

To construct Compound statements we use following connectors:
1.     NOT: This is known as negation. Example: "I am not busy" we can replace it with:
2.     AND: This is called conjunction.
 Example: Here A : “I am going to market”.
                                   B: “I am going to park”.

                       A>B: “I am going to market AND park”.

3.     OR: This is called disjunction.

Example: Here A: I will go to the market.

                        B: Amit will go to the park.

                        AVB: I will go to the market OR amit will go to the park.

4.     IF…. THEN: This is called Conditional.
Example: Here A: I want to buy cloths.
                                    B:I will go to the market.

A->B: If I want to buy cloths then I will goto market.

Now to understand the basic concepts let us take an example:
Given: p is true, q is false and r is true.
Now to determine truth value of this compound statement (
q ) ->r.

P	q	r		q	( q)->r
T	F	T	F	F	T

We construct a truth table for the given statement to determine truth value.
So here I explained about the Compound Statements and how to solve compound statements, next I will tell you about Bi Conditional Statements and if anyone want to know about Steps of Solving equations with decimals then they can refer to Internet and text books for understanding it more precisely.

Conditional in Discreet Math

Today I am going to tell you about Conditional in Discreet math. In discreet math conditional statements are one of the types of the compound statements. We can define a conditional statement as: If x and y are two statement variables, the conditional of y by x can be given as “If x then y” or “x implies y”. It is denoted as “x->y”.  It will be false in case if x is true and y is false, else it will be true. In this x is called hypothesis or antecedent and y is called conclusion or consequent of conditional statement.

We can determine x->y by the following truth table:

x	y	x->y
t	t	t
t	f	f
f	t	t
f	f	t

In a conditional statement when the “if part” of the statement is false, the whole statement will be TRUE, without worrying about the conclusion (that can be either true or false). It does not depend on the conclusion part of the statement.
For example: if 1 is equal to 2 then 2 is equal to 3.
Here we will take one more example to understand it:
1.    x->

x	y		x->
T	T	F	F
T	F	T	T
F	T	F	T
F	F	T	T

Using truth tables we can easily solve these conditional statements.
Now I am going to tell you some interesting facts about conditional statements. To represent IF…Then as OR and negation of a conditional statement we can write it as:
1.    x->y as
2.    And the negation of “if x then y” is equal to “x and not y”, that is <(x->y) equivalent to x>
In the next section I will tell you about the compound statements in discreet math.

Conjunction in discreet maths

Today I am going to tell you about the Conjunction. Conjunction is a very interesting part of discrete math, it is essentially a logical function of binary that having a two place logical operator. This function is applied on two or more logical operands which results in either false/true or 0/1. Conjunction in discreet maths always returns true (1) value if both of its operands have true value else it will return false (0). It is represented as AND. Its logical sign is >.
Here we will take some examples to understand the main concept behind this:
1.       Let there are two operands say A, B where A = 0 and B = 0 then A>B = 0.
2.       Similarly if A = 1 and B = 1 then A>B = 1.
3.       If A = 0 and B = 1 then A>B = 0 and vice versa. (To get help on icse board books click here)

So from the above examples we get to know that whenever the value of A and B is 1(TRUE) then the result or conjunction of A and B is also TRUE (1) else FALSE (0).
Similar to Disjunction (OR) it also has some properties which help us to solve questions related to this. These properties are: Consider we have 3 logical operands say A, B, C then
1.       Commutative: Conjunction of A and B is equal to the conjunction of B and C i.e. A>B = B>A.
2.       Associative: According to this property A> (B>C) = (A>B) >C.
3.       Distributive: This property has two operations AND and OR. i.e. A>(BVC) = (A>B)V(A>C).
4.       Identity potency: According to this property Conjunction of an operator to itself always results in the same operator i.e. A>A = A.
So by using these properties of conjunctions we can solve any problems related to finding conjunctions. Today we got some interesting knowledge about conjunctions. In the next topic we will discuss about the disjunctions and In the next session we will discuss about Conditional in Discreet Math.