Home / Logic / Exclusive disjunction
Truth table
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 |