MHT CET · Maths · Mathematical Reasoning
If \((p \wedge \sim r) \rightarrow(\sim p \vee q)\) has truth value ' \(F\) ', then truth values of \(p, q\) and \(r\) are respectively
- A F,F,T
- B T,T,T
- C T,F,F
- D F,F,F
Answer & Solution
Correct Answer
(C) T,F,F
Step-by-step Solution
Detailed explanation
\(\because(p \wedge \sim r) \rightarrow(\sim p \vee q)\) has truth value \(F\)
\(\Rightarrow(p \wedge \sim r)\) is \(T\) and \((\sim p \vee q)\) is \(F\)
\(\Rightarrow(P\) is \(T\) and \(\sim r\) is \(T)\) and \((\sim p\) is \(F\) and \(q\) is \(F)\)
\(\Rightarrow P\) is \(T, r\) is \(F\) and \(q\) is \(F\)
\(\Rightarrow(p \wedge \sim r)\) is \(T\) and \((\sim p \vee q)\) is \(F\)
\(\Rightarrow(P\) is \(T\) and \(\sim r\) is \(T)\) and \((\sim p\) is \(F\) and \(q\) is \(F)\)
\(\Rightarrow P\) is \(T, r\) is \(F\) and \(q\) is \(F\)
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