If and only if

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m (punct)
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: '''P''' if and only if '''Q'''
 
: '''P''' if and only if '''Q'''
 
means the same thing as:
 
means the same thing as:
: '''P''' [[implies]] '''Q''', and '''Q''' implies '''P'''
+
: '''P''' [[implies]] '''Q''', and '''Q''' implies '''P'''.
  
 
[[Category:Logic]]
 
[[Category:Logic]]

Revision as of 01:48, 30 September 2006

In logic the phrase if and only if means is logically equivalent to, or is a necessary and sufficient condition for.

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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