Exclusive or

Exclusive or is a two-place logical connective true exactly when one of its two propositions is true and the other is false.

Truth table: A table listing a logical expression’s truth value for every assignment of truth values to its variables. Its four rows define when exclusive or is true and false.
Logical proposition: A declarative statement that has a truth value, true or false. Exclusive or combines two propositions and tests their truth values.
XOR gate: A digital logic gate that outputs true when exactly one input is true. It is the hardware implementation of the exclusive-or connective.
Inclusive or: A disjunction true when at least one of its propositions is true, including when both are true. Unlike exclusive or, inclusive or accepts the case where both propositions hold.
Logical equivalence: A relation between propositions that have the same truth value under every interpretation. Exclusive or can be rewritten using equivalent formulas such as a disjunction excluding conjunction.
Logical conjunction: A connective true when both of its input propositions are true. Exclusive or rules out the joint-truth case accepted by conjunction.
Parity bit: A bit added to data so the total number of 1 bits has a chosen parity. Parity calculations use repeated exclusive-or operations to detect some transmission errors.
Set symmetric difference: The elements belonging to exactly one of two sets, but not both. Membership in the symmetric difference follows the same exactly-one condition as exclusive or.
Negation: A logical operation that reverses a proposition’s truth value. Negating a biconditional yields exclusive or: the propositions must differ in truth value.
Logical disjunction: A connective usually true when at least one input proposition is true. Exclusive or narrows disjunction by rejecting the case where both inputs are true.

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