JEE Main 2022 · 30 Jul · Shift 2, Mathematics question 80

B. $\sim(p\Rightarrow q)\equiv p\wedge\sim q$; joined with $\sim p$ it needs p and ∼p at once, so it is always false.

The others. A is $(p\Rightarrow q)\Rightarrow\sim(p\Rightarrow q)\equiv\sim(p\Rightarrow q)$, true when p is true and q false; C is true when p and q are true; D when both are false.

(B)