JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Mathematical Reasoning *

The statement $(p\Rightarrow q)\vee (p\Rightarrow r)$ simplifies to $(\sim p\vee q)\vee (\sim p\vee r)=\sim p\vee (q\vee r)=p\Rightarrow (q\vee r)$. Option (C) matches this directly. Option (A): $(p\wedge \sim r)\Rightarrow q$ is $\sim (p\wedge \sim r)\vee q=(\sim p\vee r)\vee q=\sim p\vee (q\vee r)$, which is equivalent. Option (D): $(p\wedge \sim q)\Rightarrow r$ is $\sim (p\wedge \sim q)\vee r=(\sim p\vee q)\vee r=\sim p\vee (q\vee r)$, which is equivalent. Option (B): $(\sim q)\Rightarrow ((\sim r)\vee p)$ is $q\vee (\sim r\vee p)=p\vee q\vee \sim r$, which is NOT the same as $\sim p\vee q\vee r$. Thus (B) is NOT equivalent.