View source for Exclusive or

'''Exclusive or''' or '''exclusive disjunction''' is a [[Logical connective|logical operation]] that outputs true only when inputs differ (one is true, the other is false).

== Description ==

It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true; the exclusive or operator excludes that case. This is sometimes thought of as "one or the other but not both". This could be written as "A or B, but not, A and B".

More generally, XOR is true only when an odd number of inputs are true. A chain of XORs—a XOR b XOR c XOR d (and so on)—is true whenever an odd number of the inputs are true and is false whenever an even number of inputs are true.

The negation of XOR is [[logical biconditional]], which outputs true only when both inputs are the same.

== See also ==

* [[Affirming a disjunct]]
* [[Ampheck]]
* [[Boolean algebra (logic)]]
* [[Boolean domain]]
* [[Boolean function]]
* [[Boolean-valued function]]
* [[Controlled NOT gate]]
* [[Disjunctive syllogism]]
* [[First-order logic]]
* [[Inclusive or]]
* [[Involution]]
* [[List of Boolean algebra topics]]
* [[Logical biconditional]]
* [[Logical connective]]
* [[Logical graph]]
* [[Logical value]]
* [[Material conditional]]
* [[Operation]]
* [[Paradox of material implication]]
* [[Parity bit]]
* [[Propositional calculus]]
* [[Rule 90]]
* [[Symmetric difference]]
* [[XOR cipher]]
* [[XOR gate]]
* [[XOR linked list]]

== External links ==

* [https://en.wikipedia.org/wiki/Exclusive_or Exclusive or] @ Wikipedia


[[Category:Logic]]