MHT CET · Maths · Mathematical Reasoning
The negation of \(\sim s \vee(\sim r \vee s)\) is equivalent to
- A \(s \wedge r\)
- B \(\sim r \wedge s\)
- C \(s \wedge(r \wedge \sim s)\)
- D \(s \wedge(r \vee \sim s)\)
Answer & Solution
Correct Answer
(A) \(s \wedge r\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \sim\{\sim s \vee(\sim r \wedge s)\} \equiv \sim(\sim s) \wedge\{\sim(\sim r \wedge s)\} \\ & \equiv s \wedge\{\sim(\sim r) \vee \sim s\} \\ & \equiv s \wedge\{r \vee \sim s\} \\ & \equiv(s \wedge r) \vee(s \wedge \sim s) \\ & \equiv(s \wedge r) \vee c \\ & \equiv(s \wedge r)\end{aligned}\)
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