MHT CET · Maths · Mathematical Reasoning
If truth value of logical statement \((p \leftrightarrow \sim q) \rightarrow(\sim p \wedge q)\) is false, then the truth values of \(\mathrm{p}\) and \(\mathrm{q}\) are respectively
- A \(\mathrm{F}, \mathrm{T}\)
- B \(\mathrm{T}, \mathrm{T}\)
- C \(\mathrm{T}, \mathrm{F}\)
- D \(\mathrm{F}, \mathrm{F}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{T}, \mathrm{F}\)
Step-by-step Solution
Detailed explanation
As \((p \leftrightarrow \sim q) \rightarrow(\sim p \wedge q)\) is false, we get \(p \leftrightarrow \sim q \equiv T\) and \(\sim p \wedge q \equiv F\)
\(\sim p \wedge q=F\)
\(\Rightarrow \sim \mathrm{p} \equiv \mathrm{F}\) and \(\mathrm{q} \equiv \mathrm{F}\)
\(\Rightarrow \mathrm{p} \equiv \mathrm{T}\) and \(\mathrm{q} \equiv \mathrm{F}\)
\(\sim p \wedge q=F\)
\(\Rightarrow \sim \mathrm{p} \equiv \mathrm{F}\) and \(\mathrm{q} \equiv \mathrm{F}\)
\(\Rightarrow \mathrm{p} \equiv \mathrm{T}\) and \(\mathrm{q} \equiv \mathrm{F}\)
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