Biconditional statement in Discrete mathematics
If p and q are statements, then the statement p if and only if q denoted by p ⇔ q is called a Biconditional statement and the connective if and only if is the biconditional connective. The biconditional statement p ⇔ q can also be stated as “p is a necessary and sufficient condition for q” or as “p implies q and q imply p”.
1. He swims if and only if the water is warm.
2. Sales of houses fall if and only if the interest rate rises.
The truth table of p ⇔ q is given in the below table. It may be noted that p ⇔ q is true when both p and q are true or both p and q are false.