Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R):

Assertion (A): ¬p is true.

Reason (R): p → q is true and q is false.

In the light of the above statements, choose the correct answer from the options given below:

The correct answer is : Option 1) Both (A) and (R) are true and (R) is the correct explanation of (A)

Key Points

Given:

• p → q is true
• q is false

Apply logical inference:

The implication p → q is logically equivalent to ¬p ∨ q. For p → q to be true when q is false, ¬p must be true. That means p is false.

Therefore:

• Assertion (A): ¬p is true ✅
• Reason (R): p → q is true and q is false ⇒ ¬p is true ✅
• Hence, (R) is the correct explanation of (A)

Correct Answer: Option 1) Both (A) and (R) are true and (R) is the correct explanation of (A)