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: Approach
Build a short truth table for the only row that can make the given statement false.

Step 2: Row
$\sim p\vee q=F$ needs $\sim p=F$ and $q=F$. So the row is $p=T$, $q=F$.

Step 3: Evaluate
- $p\leftrightarrow q$: T and F, so F.
- $p\to q$: T then F, so F.
- $q\to p$: F then T, so T.
Only $q\to p$ comes out true, option (C).

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