JEE Main 2022 · 28 Jun · Shift 1 · Mathematics Q20

MathematicsSingle correct+4 / -1Question 20 of 90

Let $p,q,r$ be three logical statements. Consider the compound statements

$S_1:((\sim p)\vee q)\vee((\sim p)\vee r)$ and

$S_2:p\rightarrow(q\vee r)$

Then, which of the following is NOT true ?

S_2

is True, then

S_1

is True

S_2

is False, then

S_1

is False

S_2

is False, then

S_1

is True

S_1

is False, then

S_2

is False

Answer and worked solution

Official answer: C

Simplify. $S_1=\sim p\vee q\vee r$ and $S_2=\sim p\vee(q\vee r)$ : they are equivalent, always sharing a truth value.

Not true. "If $S_2$ is False, then $S_1$ is True".

(C)

Topics:Mathematical reasoning

JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 20