Let a: ∼ p ∧ ∼ r ∨ ∼ q ∨ s and b p ∨ s ↔ q ∧ r . If the truth values of p and q are true and that of r and s are false, then the truth values of a and b are respectively…

Step-by-step solution

Key Idea Use p → q ≡ ∼ p ∨ q and p ↔ q ≡ ∼ p ∨ q ∧ p ∨ ∼ q Given, p , q → T and r , s → F ∴ a : ∼ p ∧ ∼ r ∨ ∼ q ∨ s ≡ ∼ T ∧ T ∨ F ∨ F ≡ ∼ T ∨ F ≡ F ∨ F ≡ F and b p ∨ s → q ∧ r ≡ ∼ p ∨ s ∨ q ∧ r ∧ p ∨ s ∨ ∼ q ∧ r ∵ p ↔ q ≡ ∼ p ∨ q ∧ p ∨ ∼ q ≡ ∼ T ∨ F ∨ T ∧ F ∧ T ∨ F ∨ T ∧ F ≡ F ∨ F ∧ T ∨ T ≡ F ∧ T ≡ F