Let p and q be two statements. Then ∼(p ∧(p ⇒ ∼ q)) is equivalent to

Question

Let p and q be two statements. Then ∼(p ∧(p ⇒ ∼ q)) is equivalent to (A) p ∨(p ∧ q) (B) (∼ p) ∨ q (C) p ∨(p ∧(∼ q)) (D) p ∨((∼ p) ∧ q)

Tardigrade Admin · Accepted Answer

∼( p ∧( p arrow ∼ q )) ≡ ∼ p ∨ ∼(∼ p ∨ ∼ q ) ≡ ∼ p ∨( p ∧ q ) ≡(∼ p ∨ p ) ∧(∼ p ∨ q ) ≡ t ∧(∼ p ∨ q ) ≡ ∼ p ∨ q

Q. Let $p$ and $q$ be two statements. Then $\sim (p \land (p \Rightarrow\sim q))$ is equivalent to