MHT CET · Maths · Mathematical Reasoning
If \(p \rightarrow(\sim p \vee q)\) is false, then the truth values of \(p\) and \(q\) are, respectively
- A T, F
- B F, F
- C F, T
- D T, T
Answer & Solution
Correct Answer
(A) T, F
Step-by-step Solution
Detailed explanation
\(
\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \mathrm{q}) \equiv \mathrm{F}
\)
We know that \(\mathrm{T} \rightarrow \mathrm{F} \equiv \mathrm{F}\)
\(
\therefore \mathrm{p} \equiv \mathrm{T} \text { and }(\sim \mathrm{p} \vee 1) \equiv \mathrm{F}
\)
We know that \(\mathrm{F} \vee \mathrm{F} \equiv \mathrm{F}\)
\(
\therefore \sim \mathrm{p} \equiv \mathrm{F} \text { and } \mathrm{q} \equiv \mathrm{F}
\)
Thus p, q are T, F respectively.
\mathrm{p} \rightarrow(\sim \mathrm{p} \vee \mathrm{q}) \equiv \mathrm{F}
\)
We know that \(\mathrm{T} \rightarrow \mathrm{F} \equiv \mathrm{F}\)
\(
\therefore \mathrm{p} \equiv \mathrm{T} \text { and }(\sim \mathrm{p} \vee 1) \equiv \mathrm{F}
\)
We know that \(\mathrm{F} \vee \mathrm{F} \equiv \mathrm{F}\)
\(
\therefore \sim \mathrm{p} \equiv \mathrm{F} \text { and } \mathrm{q} \equiv \mathrm{F}
\)
Thus p, q are T, F respectively.
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