JEE Main 2022 · 26 Jun · Shift 2 · Mathematics Q20

MathematicsSingle correct+4 / -1Question 20 of 90

Let $r\in\{p,q,\sim p,\sim q\}$ be such that the logical statement $r\vee(\sim p)\Rightarrow(p\wedge q)\vee r$ is a tautology. Then $r$ is equal to :

p

q

\sim p

\sim q

Answer and worked solution

Official answer: C

Try $r=\sim p$ . The statement is $\sim p\Rightarrow(p\wedge q)\vee\sim p$ , always true.

Others fail. E.g. $r=q$ with $p=q=$ F: left side T, right side F.

(C)

Topics:Mathematical reasoning

JEE Main 2022 · 26 Jun · Shift 2, Mathematics question 20