# What is a biconditional statement

## Conditional Statements

A conditional statement is any statement of the form “If P, then Q,” where P and Q are simple statements. P is called “the hypothesis,” and Q is called “the conclusion.” If you use the definitions of the previous examples of P and Q, “If P, then Q” means “If this figure is a triangle, then it has three sides.”

## Deriving New Conditional Statements

Given any conditional statement, you can always derive three other conditional statements from it, for a total of four distinct types: the original statement, its “converse,” its “inverse” and its “contrapositive.”

## The Converse of a Conditional Statement

To construct the converse of “If P, then Q,” you would simply exchange P for Q, thus obtaining “If Q, then P,” which here means “If this figure has three sides, then it is a triangle.” If a conditional statement is true, then its converse may be true, but it is not necessarily true. For example, it may be true that “If there is a major snowstorm, then they will cancel school.” But this clearly does not make it true that “If they cancel school, then there will be a major snowstorm.”