Question

If \(p\rightarrow (\sim p\vee q)\) is false, then the truth values of \(p,q\) are:

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

Hint:

An implication is false only when its antecedent is true and its consequent is false.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
\(p\rightarrow r\) is false only if \(p\) is true and \(r\) is false.

Step 2: Apply
Here \(r=\sim p\vee q\). So \(p\) is true and \(\sim p\vee q\) is false.

Step 3: Disjunction false
\(\sim p\vee q\) is false only when both \(\sim p\) and \(q\) are false.

Step 4: Solve
\(\sim p\) false gives \(p=T\), which agrees with the first condition, and \(q=F\).

Final Answer:
p is true and q is false. \[ \boxed{\text{(A) }T,F} \]