In logic and related fields such as mathematics and philosophy, "'if and only if "'( shortened "'iff "') is a biconditional logical connective between statements.
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In that it is biconditional, the connective can be likened to the standard material conditional ( " only if ", equal to " if . . . then " ) combined with its reverse ( " if " ); hence the name.
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Logical equality ( also known as biconditional ) is an operation on two logical values, typically the values of two propositions, that produces a value of " true " if and only if both operands are false or both operands are true.
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For example, " I'll buy you a new wallet if you need one " may be meant as a biconditional, since the speaker doesn't intend a valid outcome to be buying the wallet whether or not the wallet is needed ( as in a conditional ).
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The model M + h is just like the model M except that h interprets each " definiendum " according to the following biconditional, the left-hand side of which is read as G _ i ( \ overline { t } ) is true in M + h .
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The biconditional relationship above between the variance-to-mean power law and power law autocorrelation function, and the Wiener Khinchin theorem imply that any sequence that exhibits a variance-to-mean power law by the method of expanding bins will also manifest 1 / " f " noise, and vice versa.
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If " Q " proposes that " P " pay $ 10, 000 so that " Q " withholds information that would lead to " P "'s arrest, then despite the fact that the proposal is biconditional ( that is, " P " may choose to pay or not pay, which would lead to different outcomes ) it is not a throffer.
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Since the statement and the converse are both true, it is called a biconditional, and can be expressed as " "'A polygon is a quadrilateral " if, and only if, " it has four sides . "'" ( The phrase " if and only if " is sometimes abbreviated " iff " . ) That is, having four sides is both necessary to be a quadrilateral, and alone sufficient to deem it a quadrilateral.
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