JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Mathematical Reasoning *

Which of the following statement is a tautology?

Answer: (C)

Solution

A tautology is a statement that is always true.

(A)

(\sim q \land p) \land q = (\sim q \land q) \land p = F \land p = F

(not a tautology)

(B)

(\sim q \land p) \land (p \land \sim p) = (\sim q \land p) \land F = F

(not a tautology)

(C)

(\sim q \land p) \lor (p \lor \sim p) = (\sim q \land p) \lor T = T

(tautology, since

p \lor \sim p

is always true)

(D)

(p \land q) \land (\sim (p \land q)) = F

(not a tautology)

Therefore, option (C) is the tautology.

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Single correct option