Question

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

p → (p ∨ ∼ q)

Answer 1

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