If \((p \wedge \sim q) \wedge (p \wedge r) \rightarrow\ \sim p \vee q\) is false, then the truth values of \(p, q\) and \(r\) are, respectively :
Show Hint
- F, T, F
- T, F, T
- T, T, T
- F, F, F
The Correct Option is B
Solution and Explanation
B = \(\sim p \vee q\) is false: both \(\sim p\) and q are false, so p = T and q = F.
A = \((p\wedge\sim q)\wedge(p\wedge r)\) is true: with p = T, q = F we get \(p \wedge \sim q = T\), and we need \(p \wedge r = T\), so r = T.
Therefore (p, q, r) = (T, F, T).
Answer: (2) T, F, T
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