## Discrete Mathematics with Applications 4th Edition

$(P ∧ Q) ∨ Q≡ (P ∨ Q) ∧ Q$ are logically equall
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