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Biconditional Statement

A biconditional statement is a combination of a conditional statement and its converse written in the if and only if form.

Two line segments are congruent if and only if they are of equal length.

It is a combination of two conditional statements, “if two line segments are congruent then they are of equal length” and “if two line segments are of equal length then they are congruent”.

A biconditional is true if and only if both the conditionals are true.

Bi-conditionals are represented by the symbol $\leftrightarrow$ or $\Leftrightarrow$ .

$p \leftrightarrow q$ means that $p \to q$ and $q \to p$ . That is, $p \leftrightarrow q = (p \to q) \land (q \to p)$ .

Example:

Write the two conditional statements associated with the bi-conditional statement below.

A rectangle is a square if and only if the adjacent sides are congruent.

The associated conditional statements are:

a) If the adjacent sides of a rectangle are congruent then it is a square.

b) If a rectangle is a square then the adjacent sides are congruent.