JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Mathematical Reasoning *

In S1, $p\Rightarrow q$ is logically $\sim p\vee q$, while $p\wedge \sim q$ is precisely its negation; the disjunction of a statement with its own negation is always true, so S1 is a tautology. In S2, $(\sim p\Rightarrow \sim q)$ is $p\vee \sim q$ and $(\sim p\vee q)$ is $p\Rightarrow q$, so the compound is $(p\vee \sim q)\wedge (p\Rightarrow q)$; taking $p$ and $q$ both true makes it true, so it is not a contradiction and S2 is wrong. Hence only S1 is correct.