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.
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