COMEDK · Maths · 17. Mathematical Reasoning
If \((p \wedge \sim r) \rightarrow(\sim p \vee q)\) is false, then the truth values of \(p, q\) and \(r\) are respectively
- A \(\mathrm{T}, \mathrm{F}\) and \(\mathrm{T}\)
- B \(\mathrm{F}, \mathrm{T}\) and \(\mathrm{T}\)
- C \(\mathrm{F}, \mathrm{F}\) and \(\mathrm{T}\)
- D T, \(\mathrm{F}\) and \(\mathrm{F}\)
Answer & Solution
Correct Answer
(D) T, \(\mathrm{F}\) and \(\mathrm{F}\)
Step-by-step Solution
Detailed explanation
Given that, \((p \wedge \sim r) \rightarrow(\sim p \vee q)\) is false \(\Rightarrow(p \wedge \sim r)\) is true and \((\sim p \vee q)\) is false \(\Rightarrow(p\) is true and \(\sim r\) is true \()\) and ( \(\sim p\) is false and \(q\) is false) \(\Rightarrow p\) is true, \(r\)…
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