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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 |