If and only if

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↔

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⇔

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≡

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:Iff redirects here. For other meanings, see IFF.

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In mathematics, philosophy, logic and technical fields that depend on them, "if and only if" is a connective between statements which means that the truth of either one of the statements requires the truth of the other. Thus, either both statements are true, or both are false.

Related Topics:
Mathematics - Philosophy - Logic

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In writing, common alternative phrases to "if and only if" include iff, "Q is necessary and sufficient for P", "P is equivalent to Q", "P precisely if Q", and "P precisely when Q". (Many authors regard "iff" as unsuitable in formal writing; others use it freely.)

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In logical formulas, logical symbols are used instead of these phrases; see the discussion of notation.

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