Question

If the statement pattern \((p \wedge q) \rightarrow(r \vee \sim s)\) is false, then the truth values of \(p, q, r\) and \(s\) are respectively

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

Hint:

A conditional is false only when the hypothesis is true and the conclusion is false.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
\((p\wedge q)\rightarrow(r\vee\sim s)\) is false only when \(p\wedge q\) is true and \(r\vee\sim s\) is false.

Step 2: Hypothesis True
\(p\wedge q\) true means \(p=T\) and \(q=T\).

Step 3: Conclusion False
\(r\vee\sim s\) false means \(r=F\) and \(\sim s=F\), so \(s=T\).

Step 4: Result
\(p,q,r,s = T,T,F,T\), option (D).

Final Answer:
The truth values are \(T,T,F,T\). \[ \boxed{\text{(D) }T,T,F,T} \]