Sets, Relations and Function: Let triangle,nablain\wedge,vee\ be such that (pto q) triangle (p… | JEE Main 2023

JEE Main 2023 (Online) 25th January Evening ShiftQuestion 1

Let $\triangle,\nabla\in\{\wedge,\vee\}$ be such that $(p\to q)\,\triangle\,(p\,\nabla\,q)$ is a tautology. Then :

Sets, Relations and Function

$\triangle=\wedge,\nabla=\vee$$\triangle=\vee,\nabla=\wedge$$\triangle=\vee,\nabla=\vee$✓ Correct answer$\triangle=\wedge,\nabla=\wedge$

Solution

$(p\to q)\vee(p\vee q)=\sim p\vee q\vee p=T$, a tautology, while the other choices fail (e.g. $(p\to q)\vee(p\wedge q)=\sim p\vee q$). So $\triangle=\vee,\nabla=\vee$.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2023 (Online) 25th January Evening Shift)

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