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What is the negation of the statement p → (q ∧ r)?

1. ~p → ~(q ∧ r)
2. ~p ∨ (q ∧ r)
3. (q ∧ r) → p
4. p ∧ (~q ∨ ~r)

Correct answer: p ∧ (~q ∨ ~r)

Solution

Negating an implication: ~(p -> (q ∧ r)) = p ∧ ~(q ∧ r) = p ∧ (~q ∨ ~r).

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