Answer
$(P ∧ Q) ∨ Q≡ (P ∨ Q) ∧ Q $
are logically equall
Work Step by Step
The Boolean expression for (a) is (P ∧ Q) ∨ Q, and for
(b) it is (P ∨ Q) ∧ Q. We must show that if these expressions
are regarded as statement forms, then they are logically
equivalent. But
(P ∧ Q) ∨ Q
≡$ Q ∨ (P ∧ Q) $ by the commutative law for ∨
≡ $(Q ∨ P) ∧ (Q ∨ Q)$ by the distributive law
≡ $(Q ∨ P) ∧ Q $ by the idempotent law
≡ $(P ∨ Q) ∧ Q$ by the commutative law for ∧
Following the circuit
