Question

Use the table of propositional logical equivalences to show that ¬(p ∨

¬(p ∧)) is a contradiction.

Answer 1

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