logical connective From Wikipedia, the free encyclopedia
In logic and mathematics, if and only if (sometimes abbreviated as iff) is a logical operator denoting a logical biconditional (often symbolized by [1] or). It is often used to conjoin two statements which are logically equivalent.[2]
INPUT | OUTPUT | |
A | B | A B |
0 | 0 | 1 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
In general, given two statement A and B, the statement "A if and only if B" is true precisely when both A and B are true or both A and B are false.[3][4] In which case, A can be thought of as the logical substitute of B (and vice versa).[5]
An "if and only if" statement is also called a necessary and sufficient condition.[6][2] For example:
Note that the truth table shown is also equivalent to the XNOR gate.
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