If and only if
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− | In [[logic]], the phrase '''if and only if''' means "is logically equivalent to", or "is a [[necessary]] and [[sufficient]] condition for". It is often abbreviated ''' | + | In [[logic]], the phrase '''if and only if''' means "is logically equivalent to", or "is a [[necessary]] and [[sufficient]] condition for". It is often abbreviated '''iff'''. |
For any statements '''P''' and '''Q''', | For any statements '''P''' and '''Q''', |
Revision as of 18:15, 4 April 2007
In logic, the phrase if and only if means "is logically equivalent to", or "is a necessary and sufficient condition for". It is often abbreviated iff.
For any statements P and Q,
- P if and only if Q
means the same thing as:
- P implies Q, and Q implies P.