Definition:Exclusive Or

Definition
Exclusive or is a binary connective which can be written symbolically as $p \oplus q$ whose behaviour is as follows:


 * $p \oplus q$

means:
 * Either $p$ is true or $q$ is true but not both.

or symbolically:
 * $p \oplus q := \paren {p \lor q} \land \neg \paren {p \land q}$

where $\land$ denotes the and operator and $\lor$ denotes the or operator.

There is no standard symbol for this, but the one shown above is seen commonly enough to be adopted as standard for this site.

Also see

 * Exclusive Or is Negation of Biconditional
 * Non-Equivalence