Answer
(a) Distributive Law
(b) Commutative Law
(c) Negation Law
(d) Identity Law
Work Step by Step
Distributive law states p ∧ (r ∨ q) ≡ (p ∧ r) ∨ (p ∧ q) . Replace r with ∼q and apply the law to get (p ∧ ∼q) ∨ (p ∧ q) ≡ p ∧ (∼q ∨ q).
Commutative law states p ∨ q ≡ q ∨ p . Apply the law in p ∧ (∼q ∨ q) to get p ∧ (q ∨ ∼q).
Negation law states p ∨ ∼p ≡ t . So p ∧ (q ∨ ∼q) becomes p ∧ t.
Identity law states p ∧ t ≡ p. Hence we get (p ∧ ∼q) ∨ (p ∧ q) ≡ p.
