Question

Using the rule of negation write the negation of the following with justification.

(∼ p ∨ ∼ q) ∨ (p ∧ ∼ q)

Answer 1

The negation of (∼ p ∨ ∼ q) ∨ (p ∧ ∼ q) is
∼ [(∼ p ∨ ∼ q) ∨ (p ∧ ∼ q)] ≡ ∼ (∼ p ∨ ∼ q) ∧ ∼ (p ∧ ∼ q) ..............(Negation of disjunction)
≡ [∼ (∼ p) ∧ ∼ (∼ q)] ∧ [∼ p ∨ ∼ (∼ q)] ...(Negation of disjunction and conjunction)
≡ (p ∧ q) ∧ (∼ p ∨ q) ...........(Negation of negation)