MHT CET · Maths · Mathematical Reasoning
If \(\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \mathrm{q})\) is false, then the truth values of \(\mathrm{p}\) and \(\mathrm{q}\) are respectively
- A F, T
- B F, F
- C T, T
- D T, F
Answer & Solution
Correct Answer
(D) T, F
Step-by-step Solution
Detailed explanation
(D)
We know that \(\mathrm{T} \rightarrow \mathrm{F}\) is false.
\(\therefore \mathrm{p}\) must be true and \((\sim \mathrm{p} \vee \mathrm{q})\) must be false. \(\Rightarrow \mathrm{p}\) is true.
We know that \(\mathrm{F} \vee \mathrm{F}\) is false.
So \(\mathrm{q}\) must be false.
We know that \(\mathrm{T} \rightarrow \mathrm{F}\) is false.
\(\therefore \mathrm{p}\) must be true and \((\sim \mathrm{p} \vee \mathrm{q})\) must be false. \(\Rightarrow \mathrm{p}\) is true.
We know that \(\mathrm{F} \vee \mathrm{F}\) is false.
So \(\mathrm{q}\) must be false.
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