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.

Words : Symbols : p if and only if q p \Leftrightarrow q

A definition can be written as a biconditional statement. Consider the definition of complementary angles. Two angles whose measures have a sum of

9 0^{\circ}

are called complementary angles. The hypothesis

p

and conclusion

q

can be written as follows.

p : q : Two angles are complementary Their measures have a sum of 9 0^{\circ}

After identifying the parts, the definition can be written as a single biconditional statement.

	Statement
Conditional $p \Rightarrow q$	If $two angles are complementary,$ $then their measures have a sum of 9 0^{\circ} .$
Converse $q \Rightarrow p$	If $the measures of two angles have$ $a sum of 9 0^{\circ},$ then $the angles are complementary .$
Biconditional $p \Leftrightarrow q$	$Two angles are complementary$ if and only if $their measures have a sum of 9 0^{\circ} .$

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
$p$	$q$	$p \Leftrightarrow q$
T	T	T
T	F	F
F	T	F
F	F	T

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