Question

Negation of the compound proposition : If I study hard, then I will pass.

• A. I will study hard and I will pass.
• B. I will study hard and I will not pass.
• C. I will study hard or I shall pass.
• D. I will study hard or I shall not pass.

Answer 1

The correct option is B I will study hard and I will not pass.

Let $p$: I study hard.
$q$: I will pass.

We know that, $\sim (p\Rightarrow q)=p\wedge \sim q$
So we have negation of the compound proposition as "I will study hard and I will not pass."