# Exclusive Or as Disjunction of Conjunctions/Proof 1

From ProofWiki

## Theorem

- $p \oplus q \dashv \vdash \left({\neg p \land q}\right) \lor \left({p \land \neg q}\right)$

## Proof

\(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(\displaystyle p \oplus q\) | \(\dashv \vdash\) | \(\displaystyle \) | \(\displaystyle \neg \left ({p \iff q}\right)\) | \(\displaystyle \) | \(\displaystyle \) | Exclusive Or is Negation of Biconditional | ||

\(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(\displaystyle \) | \(\dashv \vdash\) | \(\displaystyle \) | \(\displaystyle \left({\neg p \land q}\right) \lor \left({p \land \neg q}\right)\) | \(\displaystyle \) | \(\displaystyle \) | Non-Equivalence as Disjunction of Conjunctions |

$\blacksquare$