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\section*{Equations And Proof}
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Proving $(q \Leftrightarrow (\neg p \lor \neg q)) \Leftrightarrow (\neg p \land q)$
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$q \Leftrightarrow (\neg p \lor \neg q)$ \\
$(q \land (\neg p \lor \neg q)) \lor (\neg q \land \neg(\neg p \lor \neg q))$ & Equivalence \\
$(q \land (\neg p \lor \neg q)) \lor (\neg q \land (\neg\neg p \land \neg\neg q))$ & DeMorgan \\
$ (q \land (\neg p \lor \neg q)) \lor (\neg q \land (p \land q)) $ & Double Negation \\
$(q \land (\neg p \lor \neg q)) \lor (\bot \land p) $ & Complement \& Associative \\
$(q \land (\neg p \lor \neg q))$ & $(\bot \land p)$ Bottom Always False \\
$(q \land \neg p) \lor (q \land \neg q)$ & Distributive \\
$q \land \neg p$ \\
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Therefore $(q \Leftrightarrow (\neg p \lor \neg q)) \Leftrightarrow (\neg p \land q)$
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