EDGE Math 8

BICONDITIONAL STATEMENTS

There are instances when a conditional statement and its converse are both true. This usually happens when defining terms.

Definition

The statement "p if and only if q" is a biconditional statement.

A biconditional statement "p if and only if q" is true when both the implications "If p, then q" and "If q, then p" are true.

Truth Table of Biconditional Statements

Example

Determine if each biconditional statement is true or false.

1.	Angles A and B are right angles if and only if $∠ A$ and $∠ B$ are congruent.
2.	An angle is a right angle if and only if it measures 90°.

Solution

1.	The conditional statement "If $∠ A$ and $∠ B$ are right angles, then $∠ A$ and $∠ B$ are congruent" is true but its converse is false. Thus, the biconditional statement is false.

2.	The biconditional statement is true since the implications "If an angle is a right angle, then it measures 90°" and "If an angle measures 90°, then it is a right angle" are both true. In fact, this is the definition of a right angle.