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Concept

# Biconditional Statement

A biconditional statement is a statement that combines a conditional statement and its converse. A biconditional statement contains the phrase if and only if.
A definition can be written as a biconditional statement. Consider the definition of complementary angles. Two angles whose measures have a sum of are called complementary angles. The hypothesis and conclusion can be written as follows.
After identifying the parts, the definition can be written as a single biconditional statement.
Statement
Conditional
If
Converse
If then
Biconditional
if and only if

A biconditional statement is true if and only if the conditional and its converse have the same truth value. This can be explained using the truth table for a biconditional.

Biconditional Statement
T T T
T F F
F T F
F F T