A binary logical connective, denoted
\[\begin{equation*} P \oplus Q \end{equation*} \]
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)
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"))
\(P\) | \(Q\) | \(P \oplus Q\) |
---|---|---|
false | false | false |
false | true | true |
true | false | true |
true | true | false |