Q29 / 75 · JEE Main 2020 (02 Sep Shift 2) · Mathematics

Which of the following is a tautology?

Solution

$(A)$ $~ p \land (p \lor q) \to q$

$(~ p \land p) \lor (~ p \land q) \to q$

$c \lor (~ p \land q) \to q$ (where $c$ is contradiction)

$(~ p \land q) \to q$

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

$= (p \lor ~ q) \lor q = p \lor t = t$

$(C)$ $(~ q) \lor (p \land q) \to q$

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

$= (~ q \lor p) \to q$

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

$(B)$ and $(D)$

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