The negation of the Boolean expression p ∨(∼ p ∧ q ) is equivalent to

Question

The negation of the Boolean expression p ∨(∼ p ∧ q ) is equivalent to (A) ∼ p ∨ ∼ q (B) ∼ p ∨ q (C) ∼ p ∧ ∼ q (D) p ∧ ∼ q

Tardigrade Admin · Accepted Answer

Negation of φ ∨(∼ p ∧ q) p ∨(∼ p ∧ q )=( p ∨ ∼ p ) ∧( p ∨ q ) =( T ) ∧( p ∨ q ) =( p ∨ q ) now negation of ( p ∨ q ) is ∼( p ∨ q )=∼ p ∧ ∼ q

Q. The negation of the Boolean expression $p \lor (\sim p \land q)$ is equivalent to