Question

Let p, q and r be any three logical statements. Which of the following is true?

Options

• ∼[p ∧ (∼ q)] ≡ (∼ p) ∧ q

• ∼[(p ∨ q) ∧ (∼ r) ≡ (∼ p) ∨ (∼ q) ∨ (∼ r)

• ∼[p ∨ (∼ q)] ≡ (∼ p)∧ q

• ∼[p ∨ (∼ q)] ≡ (∼ p)∧ ∼ q

Answer 1

∼[p ∨ (∼ q)] ≡ (∼ p)∧ q

Explanation:

∼[p ∨ (∼ q)] = (∼ p) ∧ ∼ (∼ q) = (∼ p) ∧ q