\begin{definition}[Definition:Exclusive Or]
'''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.
\end{definition}