MHT CET · Maths · Mathematical Reasoning
If \(\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \sim \mathrm{q})\) is false, then the truth values of \(p\) and \(q\) are respectively
- A F, F
- B \(\mathrm{F}, \mathrm{T}\)
- C \(\mathrm{T}, \mathrm{T}\)
- D \(\mathrm{T}, \mathrm{F}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{T}, \mathrm{T}\)
Step-by-step Solution
Detailed explanation
- Consider option (C)
\(\begin{aligned}
& p \rightarrow(\sim p \vee \sim q) \\
& \equiv T \rightarrow(\sim T \vee \sim T) \\
& \equiv T \rightarrow(F \vee F) \\
& \equiv T \rightarrow F \\
& \equiv F
\end{aligned}\)
\(\therefore \quad\) Option (C) is the correct answer.
\(\begin{aligned}
& p \rightarrow(\sim p \vee \sim q) \\
& \equiv T \rightarrow(\sim T \vee \sim T) \\
& \equiv T \rightarrow(F \vee F) \\
& \equiv T \rightarrow F \\
& \equiv F
\end{aligned}\)
\(\therefore \quad\) Option (C) is the correct answer.
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