JEE 2023 — Mathematics PYQ

Solution

Step 1: Simplify the inner expression

Using the distributive law:

Since $(q\vee \sim q)$ is a Tautology ($T$):

Step 2: Find the negation

We need $\sim (q\vee p)$. Using De Morgan's Law:

This is equivalent to $(\sim p)\wedge (\sim q)$.

Correct Option: (4)