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MHT CET · Maths · Mathematical Reasoning

The logical statement \([\sim(\sim \mathrm{p} \vee \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{r}) \wedge(\sim \mathrm{q} \wedge \mathrm{r})]\) is equivalent to

  1. A \((p \wedge r) \wedge \sim q\)
  2. B \((\sim \mathrm{p} \wedge \sim \mathrm{q}) \wedge \mathrm{r}\)
  3. C \(\sim \mathrm{p} \vee \mathrm{r}\)
  4. D \((p \wedge \sim q) \vee r\)
Verified Solution

Answer & Solution

Correct Answer

(A) \((p \wedge r) \wedge \sim q\)

Step-by-step Solution

Detailed explanation

\(\sim(\sim \mathrm{p} \vee \mathrm{q}) \equiv \mathrm{p} \wedge \sim \mathrm{q}\) \([\ (\mathrm{p} \wedge \sim \mathrm{q}) \vee (\mathrm{p} \wedge \mathrm{r}) \ ] \wedge (\sim \mathrm{q} \wedge \mathrm{r})\)