Question

If \(\sim p∨q\) is false then which of the following is correct?

• A. \(p\leftrightarrow q\) is \(T\)
• B. \(p\rightarrow q\) is \(T\)
• C. \(q\rightarrow p\) is \(T\)
• D. \(q\rightarrow p\) is \(F\)

Hint:

A disjunction is false only when both parts are false.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
An OR statement is false only when both components are false.

Step 2: Find the truth values
\(\sim p\vee q\) is false, so \(\sim p\) is F and \(q\) is F. So \(p\) is T and \(q\) is F.

Step 3: Check each option
(A) \(p\leftrightarrow q\) is T only when both have equal values. Here T and F differ, so it is F.
(B) \(p\to q\) with p = T and q = F is F.
(C) \(q\to p\) with q = F is T, because a false antecedent makes the implication true. So (C) is correct.
(D) \(q\to p\) is F is the opposite of (C), so it is wrong.

Final Answer:
With p true and q false, the implication q to p is true, option (C). \[ \boxed{q\rightarrow p\ \text{is T}} \]