Mathematical Reasoning: If square,lozengein\wedge,vee\ such that (sim qwedge p)\ square\ (q\… | JEE Main 2021

JEE Main 2021 (Online) 3rd August Morning ShiftQuestion 1

If $\square,\lozenge\in\{\wedge,\vee\}$ such that $(\sim q\wedge p)\ \square\ (q\ \lozenge\ \sim p)$ is a tautology, then

Mathematical Reasoning

$\square=\wedge$ and $\lozenge=\wedge$$\square=\wedge$ and $\lozenge=\vee$$\square=\vee$ and $\lozenge=\wedge$$\square=\vee$ and $\lozenge=\vee$✓ Correct answer

Solution

$(\sim q\wedge p)\vee(q\vee\sim p)=\sim(\sim p\vee q)\vee(\sim p\vee q)$, which is a tautology. With $\wedge$ in either place it fails at some row.

Mathematical Reasoning - JEE Mathematics question (JEE Main 2021 (Online) 3rd August Morning Shift)

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