The logical statement ~~p∨q∨p∧r∧~q∧r is equivalent to

Correct answer: (B) p∧r∧~q. ~~p∨q∨p∧r∧~q∧r =p∧~q∨p∧r∧~q∧r By distributive law =p∧~q∨r∧~q∧r p∧~q∧r≡p∧r∧~q =p∧∼q∧r By Associative law =p∧r∧~q

Q56 / 90 · JEE Main 2019 (09 Jan Shift 2) · Mathematics

The logical statement $[~ (~ p \lor q) \lor (p \land r)] \land (~ q \land r)$ is equivalent to

$[~ (~ p \lor q) \lor (p \land r)] \land (~ q \land r)$

$= [(p \land ~ q) \lor (p \land r)] \land (~ q \land r)$

By distributive law

$= p \land (~ q \lor r) \land (~ q \land r)$

$p \land (~ q \land r) \equiv (p \land r) \land ~ q$

$= p \land \sim q \land r$

By Associative law

$= (p \land r) \land ~ q$

Hence, the correct answer is option: 'B'.