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: Understanding the Concept
The contrapositive of \(A\to B\) is \(\sim B\to\sim A\), and it is logically equivalent to the original.

Step 2: Apply
Here \(A=\sim q\) and \(B=p\). So the contrapositive is
\[ \sim p\to\sim(\sim q)=\sim p\to q \]

Step 3: Convert to OR
An implication \(X\to Y\) is equivalent to \(\sim X\vee Y\). So
\[ \sim p\to q\equiv\sim(\sim p)\vee q=p\vee q \]

Step 4: Check the options
(A) \(p\to q\) is \(\sim p\vee q\), which differs. (B) \(p\wedge q\) is stronger. (D) \(\sim p\to\sim q\) is not equivalent. The match is (C).

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