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.