The logical proposition (∼ (∼ p ∨ q)) ∨ (p ∧ r)∧ (∼ q ∧ r) is equivalent to

Question

The logical proposition (∼ (∼ p ∨ q)) ∨ (p ∧ r)∧ (∼ q ∧ r) is equivalent to (A) (∼ p ∧ ∼ q)∧ r (B) (p ∧ r)∧ ∼ q (C) (p ∧ ∼ q)∨ r (D) ∼ p∨ r

Tardigrade Admin · Accepted Answer

[∼ (∼ p ∨ q) ∨ (p ∧ r)]∧ (∼ q ∧ r) =[(p ∧ ∼ q) ∨ (p ∧ r)]∧ (∼ q ∧ r) By distributive law =p∧ (∼ q ∨ r)∧ (∼ q ∧ r) Solution

undefined p∧ ∼ q∧ r =p∧ ∼ q∧ r By Associative law =(p ∧ r)∧ ∼ q

Q. The logical proposition $(\sim (\sim p \lor q)) \lor (p \land r) \land (\sim q \land r)$ is equivalent to