The statement pattern (p ∧ q) ∧ [∼ r ∨ (p ∧ q)] ∨ (∼ p ∧ q) is equivalent t o ............

Question

The statement pattern (p ∧ q) ∧ [∼ r ∨ (p ∧ q)] ∨ (∼ p ∧ q) is equivalent t o ............ (A) r (B) q (C) (p ∧ q)  (D) p

Tardigrade Admin · Accepted Answer

We have, (p ∧ q) ∧[∼ r ∨(p ∧ q)] ∨(∼ p ∧ q) ≡(p ∧ q) ∨(∼ p ∧ q) ≡(p ∨ ∼ p) ∧ q ≡ T ∧ q=q

Q. The statement pattern $(p \land q) \land [\sim r \lor (p \land q)] \lor (\sim p \land q)$ is equivalent t o ............