Mathematical Reasoning: The statement sim[pvee(sim(pwedge q))] is equivalent to | JEE Main 2023

JEE Main 2023 (Online) 10th April Evening ShiftQuestion 1

The statement $\sim[p\vee(\sim(p\wedge q))]$ is equivalent to

Mathematical Reasoning

$(\sim(p\wedge q))\wedge q$$\sim(p\vee q)$$(p\wedge q)\wedge(\sim p)$✓ Correct answer$\sim(p\wedge q)$

Solution

$\sim[p\vee\sim(p\wedge q)]=\sim p\wedge(p\wedge q)$, a contradiction, equivalent to $(p\wedge q)\wedge\sim p$.

Mathematical Reasoning - JEE Mathematics question (JEE Main 2023 (Online) 10th April Evening Shift)