Exclusive Or as Disjunction of Conjunctions/Proof 1
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Theorem
- $p \oplus q \dashv \vdash \paren {\neg p \land q} \lor \paren {p \land \neg q}$
Proof
\(\ds p \oplus q\) | \(\dashv \vdash\) | \(\ds \neg \left ({p \iff q}\right)\) | Exclusive Or is Negation of Biconditional | |||||||||||
\(\ds \) | \(\dashv \vdash\) | \(\ds \left({\neg p \land q}\right) \lor \left({p \land \neg q}\right)\) | Non-Equivalence as Disjunction of Conjunctions |
$\blacksquare$