Among the statements (S1): \((p \Rightarrow q) \vee((\sim p) \wedge q)\) is a tautology (S2): \((q \Rightarrow p) \Rightarrow((\sim p) \wedge q)\) is a contradiction

(A) neither (S1) and (S2) is True

(D) both (S1) and (S2) are True

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Mathematical Reasoning *

Among the statements
(S1):

(p \Rightarrow q) \lor ((\sim p) \land q)

is a tautology
(S2):

(q \Rightarrow p) \Rightarrow ((\sim p) \land q)

is a contradiction

Answer: (A)

Construct truth tables for both statements. For (S1):

(p \to q) \lor ((\sim p) \land q)

has truth values T, F, T, T for the four combinations of p and q, so it is not a tautology. For (S2):

(q \to p) \to ((\sim p) \land q)

has truth values F, F, T, F, so it is not a contradiction. Therefore neither statement is true.

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Single correct option