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.


rc Words: & p if and only if q Symbols: & p ⇔ q

A definition can be written as a biconditional statement. Consider the definition of complementary angles. Two angles whose measures have a sum of 90 ^(∘) are called complementary angles. The hypothesis p and conclusion q can be written as follows. p:& Two angles are complementary [0.4em] [-0.8em] q:& Their measures have a sum of90^(∘) After identifying the parts, the definition can be written as a single biconditional statement.

Statement
Conditional
p⇒ q
If two angles are complementary, then their measures have a sum of90^(∘).
Converse
q ⇒ p
If the measures of two angles have a sum of90^(∘), then the angles are complementary.
Biconditional
p⇔ q
Two angles are complementary if and only if their measures have a sum of90^(∘).

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 ⇔ q
T T T
T F F
F T F
F F T
Exercises