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exclusive-OR operation The logical connective combining two statements, truth values, or formulas P and Q in such a way that the outcome is true if either P or Q (but not both P and Q) is true, as shown in the table. Since the outcome is true precisely when the operands are different, it is sometimes referred to as the nonequivalence operation. It can be represented in a variety of ways, the more common methods being XOR, xor, and ∨. See also OR operation.