Sets, Relations and Function: Consider: S1: (pRightarrow q)vee(pwedgesim q) is a tautology. S2:… | JEE Main 2023

JEE Main 2023 (Online) 31st January Morning ShiftQuestion 1

Consider: S1: $(p\Rightarrow q)\vee(p\wedge\sim q)$ is a tautology. S2: $(\sim p\Rightarrow\sim q)\wedge(\sim p\vee q)$ is a contradiction. Then

Sets, Relations and Function

only S2 is correctboth S1 and S2 are correctboth S1 and S2 are wrongonly S1 is correct✓ Correct answer

Solution

$p\wedge\sim q\equiv\sim(p\Rightarrow q)$, so S1 is $X\vee\sim X$, a tautology. $(\sim p\Rightarrow\sim q)\wedge(\sim p\vee q)=(p\vee\sim q)\wedge(\sim p\vee q)\equiv p\Leftrightarrow q$, which is not a contradiction. Only S1 is correct.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2023 (Online) 31st January Morning Shift)

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