If and only if

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A B A \iff B
0 0 1
0 1 0
1 0 0
1 1 1

Iff (if and only if) means that two statements are "biconditional". "A IFF B" means that "A" is true if "B" is, and "B" is true if "A" is. This means that A "=" (has the same boolean value as) B. The truth table of iff is the same as the truth table for XNOR. For example, the sentence "Two rational numbers are equal IF AND ONLY IF ad = bc." is a biconditional statement, containing IF AND ONLY IF, or IFF. The statement "a iff b" is often notated as a \iff b.