JEE Main · 2022 · 26 Jun 2022 · Shift 2 · Mathematical Reasoning *

Testing each option by constructing truth tables, we find that when $r=\sim p$, the implication $r\vee (\sim p)\Rightarrow (p\wedge q)\vee r$ is always true (all rows yield T).

For $r=\sim p$: $r\vee (\sim p)=\sim p\vee \sim p=\sim p$, and $(p\wedge q)\vee r=(p\wedge q)\vee \sim p$. The implication $\sim p\Rightarrow (p\wedge q)\vee \sim p$ is a tautology because whenever $\sim p$ is true, $(p\wedge q)\vee \sim p$ is also true.

Answer: (C)