Exclusive disjunction

Define

A binary logical connective, denoted

\[\begin{equation*}
  P \neq Q
  \quad \text{or} \quad
  P \oplus Q
\end{equation*}
\]

and read

that is ‘true’ if and only if

so equivalent to

\[\begin{equation*}
  (P \land \lnot Q) \lor (\lnot P \land Q).
\end{equation*}
\]

(Levin, 2021, sec. 0.2; Poole & Mackworth, 2017, sec. 5.1)

Name

• Exclusive or

Explore

Construct the truth table for the statement

\[\begin{equation*}
  P \oplus Q \> \equiv \> (P \land \lnot Q) \lor (\lnot P \land Q).
\end{equation*}
\]

<<scheme/org-truth-table>>
(org-truth-table (lambda (p q)
                   (or (and p (not q))
                       (and (not p) q)))
                 '("P" "Q" "P \\oplus Q"))