Let $p, q, r$ be three statements such that the truth value of $(p \wedge q) \rightarrow(\sim q \vee r)$ is $F$. Then the truth values of $p, q, r$ are respectively:

(D) $\mathrm{T}, \mathrm{T}, \mathrm{T}$

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Mathematical Reasoning *

Let

p, q, r

be three statements such that the truth value of

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

F

. Then the truth values of

p, q, r

are respectively:

Answer: (B)

An implication is false only when its hypothesis is true and its conclusion false. So

p \land q

must be true, forcing both

p

and

q

true, while

\sim q \lor r

must be false, forcing both

\sim q

and

r

false. With

q

true,

\sim q

is already false, which is consistent, and

r

must be false. The truth values are

p = T

q = T

r = F

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Single correct option