Question

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

• A. F, T, F
• B. F, T, T
• C. T, T, F
• D. F, F, T

Hint:

Remember: an implication is false only in the case True \(\rightarrow\) False.

Answer 1

The Correct Option is A

Step 1: Condition for implication to be false.
An implication \(A\rightarrow B\) is false only when \(A\) is true and \(B\) is false.
Step 2: Apply to the given statement.
Here, \(A=(\sim p \wedge q)\) and \(B=r\).
So, \((\sim p \wedge q)\) must be true and \(r\) must be false.
Step 3: Determine truth values.
\(\sim p\) is true \(\Rightarrow p\) is false.
\(q\) must be true.
\(r\) must be false.
Step 4: Final conclusion.
Thus, the truth values are \[ p=F,\quad q=T,\quad r=F \]