# Bi Conditional Statement

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A bi-conditional statement is a logical statement which is formed by the combination of two conditional statements. A bi-conditional statement is formed when a conditional statement and its converse are put together and are checked accordingly whether the sentence is true or false.

Example 1: Given ifAnna is the mother of Regan, and then Regan is the daughter of Anna. Explain whether the statement is bi-conditional or not.

Given statement: If Anna is the mother of Regan, then Regan is the daughter of Anna.

We can rewrite the above statement also as:

If Regan is the daughter of Anna, then Anna is the mother of Regan.

Now let, Statement p = Anna is the mother of Regan.

Statement q = Regan is the daughter of Anna.

Then we can say that p ==> q is the same thing as q ==> p.

Hence, we can say that Anna is the mother of Regan if and only if Regan is the daughter of Anna.

Hence p <==> q means that the statement is bi-conditional.

Example 2: Given if 4 + 5 = 9, then ‘9’ can be written as the sum of ‘4’ and ‘5’. Is this a bi-conditional statement?

Statement p: 4 + 5 = 9

Statement q: 9 = Sum of 4 and 5

Here we can say that, 4 + 5 = 9 if and only if ‘9’ can be written as the sum of ‘4’ and ‘5’.

Hence p <==> qmeans that the statement is bi-conditional.