Question

If \(p\Rightarrow(\sim p\vee q)\) is false, then the truth value of \(p\) and \(q\) are respectively

• A. \(F,T\)
• B. \(F,F\)
• C. \(T,F\)
• D. \(T,T\)

Hint:

Implication \(P\Rightarrow Q\) is false only when \(P\) is true and \(Q\) is false.

Answer 1

The Correct Option is C

Step 1: Recall when implication is false.
\[ P\Rightarrow Q \text{ is false only when } P=T \text{ and } Q=F \]
So we must have:
\[ p=T \]
and
\[ (\sim p\vee q)=F \]
Step 2: Make \((\sim p\vee q)\) false.
OR statement is false only if both parts are false:
\[ \sim p = F \quad \text{and} \quad q=F \]
Step 3: \(\sim p = F\Rightarrow p=T\).
So:
\[ p=T,\quad q=F \]
Final Answer:
\[ \boxed{(T,F)} \]