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 implication)
≡ (p ∨ ∼ q) ∧ [∼ p ∨ ∼ (∼ q)] .............(Negation of conjunction)
≡ (p ∨ ∼ q) ∧ (∼ p ∨ q) .........(Negation of negation)