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MHT CET · Maths · Mathematical Reasoning

The negation of \(\sim s \vee(\sim r \vee s)\) is equivalent to

  1. A \(s \wedge r\)
  2. B \(\sim r \wedge s\)
  3. C \(s \wedge(r \wedge \sim s)\)
  4. D \(s \wedge(r \vee \sim s)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(s \wedge r\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \sim\{\sim s \vee(\sim r \wedge s)\} \equiv \sim(\sim s) \wedge\{\sim(\sim r \wedge s)\} \\ & \equiv s \wedge\{\sim(\sim r) \vee \sim s\} \\ & \equiv s \wedge\{r \vee \sim s\} \\ & \equiv(s \wedge r) \vee(s \wedge \sim s) \\ & \equiv(s \wedge r) \vee c \\ & \equiv(s \wedge r)\end{aligned}\)