if and only if
The phrase "if and only if" is often abbreviated as "iff" and denotes a logical biconditional, indicating that two statements are equivalent.
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Definition
C1Logic
(technical, academic)A logical operator indicating that two statements are true or false together, establishing their equivalence.
Example
- A number is even if and only if it is divisible by 2.
C1Mathematics
(technical, academic)A condition where one statement is true exactly when another statement is true, and false when the other is false.
Example
- A shape is a square if and only if it has four equal sides and four right angles.
C1Philosophy
(technical, academic)A conjunction used to express that two propositions are necessary and sufficient conditions for each other.
Example
- The statement 'I think, therefore I am' holds if and only if thinking implies existence.