MHT CET · Maths · Mathematical Reasoning
If \((p \wedge \sim r) \rightarrow(\sim p \vee q)\) has truth value False, then truth values of \(p, q, r\) are respectively.
- A F, F, T
- B F, T, F
- C T, F, F
- D \(\quad \mathrm{T}, \mathrm{T}, \mathrm{F}\)
Answer & Solution
Correct Answer
(C) T, F, F
Step-by-step Solution
Detailed explanation
Given that
\(\begin{array}{ll}
& (p \wedge \sim r) \rightarrow(\sim p \vee q) \equiv F \\
\therefore & \sim p \vee q \equiv F \\
\therefore & \sim p \equiv F \text { and } q \equiv F \\
\therefore & p=T \text { and } q=F \\
\therefore & \text { Option }(C) \text { is correct. }
\end{array}\)
\(\begin{array}{ll}
& (p \wedge \sim r) \rightarrow(\sim p \vee q) \equiv F \\
\therefore & \sim p \vee q \equiv F \\
\therefore & \sim p \equiv F \text { and } q \equiv F \\
\therefore & p=T \text { and } q=F \\
\therefore & \text { Option }(C) \text { is correct. }
\end{array}\)
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