Q65 / 120 · VITEEE 2014 · Mathematics

The negation of $(\sim p \wedge q) \vee(p \wedge \sim q)$ is

  • A
    $(\mathrm{p} \vee \sim \mathrm{q}) \vee(\sim \mathrm{p} \vee \mathrm{q})$
  • Correct answer
    B
    $(\mathrm{p} \vee \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$
  • C
    $(\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$
  • D
    $(p \wedge \sim q) \wedge(p \vee \sim q)$

Solution

Let $S:\left(\sim p^{\wedge} q\right) \vee(p \wedge \sim q)$ $\Rightarrow \sim S: \sim\left[\left(\sim p^{\wedge} q\right) \vee(p \wedge \sim q)\right]$ $\Rightarrow \sim S: \sim\left(\sim p^{\wedge} q\right) \wedge \sim(p \wedge \sim q)$ $\Rightarrow \sim S:(p \vee \sim q) \wedge(\sim p \vee q)$

Hence, the correct answer is option: 'B'.

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