Question

The contrapositive of \(\sim q\rightarrow p\) is equivalent to

• A. \(p\rightarrow q\)
• B. \(p∧q\)
• C. \(p∨q\)
• D. \(\sim p\rightarrow \sim q\)

Hint:

The contrapositive of A implies B is not-B implies not-A.

Answer 1

The Correct Option is C

Step 1: Approach
Simplify the original statement first; any equivalent form is fine, and the contrapositive is equivalent.

Step 2: Original
$\sim q\to p\equiv\sim(\sim q)\vee p=q\vee p$.

Step 3: Contrapositive
Since a statement and its contrapositive are equivalent, the contrapositive is also $p\vee q$.

Step 4: Truth-table check
$p\vee q$ is false only when both are false. $\sim q\to p$ is false when $\sim q$ is T and $p$ is F, that is q = F and p = F. The two agree, so option (C).

Final Answer:
The contrapositive is equivalent to $p\vee q$, option (C). \[ \boxed{p\vee q} \]