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''.
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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 '''[[iff]]'''.
  
 
For any statements '''P''' and '''Q''',
 
For any statements '''P''' and '''Q''',

Revision as of 17:15, 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.
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