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Archangel Macsika

Use the table of propositional logical equivalences to show that ¬(p ∨ ¬(p ∧)) is a contradiction.

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\neg(p\vee \neg(p\wedge q)\\ \iff \neg p \wedge \neg(\neg(p \wedge q) \text{ De Morgan's Law}\\ \iff \neg p \wedge(p \wedge q) \text{ Double Negation Law}\\ \iff (\neg p\wedge p) \wedge q \text{ Associativity Law}\\ \iff F \wedge q \text{ Contradiction}\\ \iff F \text{ Domination Law}\\ \text{Hence the statement is a Contradiction.}

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Question ID: mtid-5-stid-8-sqid-3155-qpid-1854