If and only if
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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.