Explanation
Solution
Step 1: Negate the consequent (∼B)
We need to find the negation of (∼q→∼r).
Recall the identity for the negation of a conditional: ∼(P→Q)≡P∧∼Q.
Applying this:
Step 2: Negate the antecedent (∼A)
Step 3: Form the contrapositive (∼B→∼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 ∼B→∼A directly:
If we apply contrapositive logic inside the bracket first (∼q→∼r≡r→q), the statement becomes p→(r→q). Its contrapositive would be:
Final Answer:
The contrapositive is: