JAMIA 2023 — Mathematics PYQ

Step 1: Negate the consequent ($\sim B$)

We need to find the negation of $(\sim q\to \sim r)$.

Recall the identity for the negation of a conditional: $\sim (P\to Q)\equiv P\wedge \sim Q$.

Applying this:

Step 2: Negate the antecedent ($\sim A$)

Step 3: Form the contrapositive ($\sim B\to \sim A$)

Substitute the results from Step 1 and Step 2:

3. Alternative Form (Using the conditional form)

Sometimes options are given without simplifying the negation of $B$. If we keep it in the form $\sim B\to \sim A$ directly:

If we apply contrapositive logic inside the bracket first ($\sim q\to \sim r\equiv r\to q$), the statement becomes $p\to (r\to q)$. Its contrapositive would be:

Final Answer:

The contrapositive is: