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

The negation of $(\sim p \wedge q) \vee(p \wedge \sim q)$ is
  1. $(\mathrm{p} \vee \sim \mathrm{q}) \vee(\sim \mathrm{p} \vee \mathrm{q})$
  2. $(\mathrm{p} \vee \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$
  3. $(\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$
  4. $(p \wedge \sim q) \wedge(p \vee \sim q)$

Solution

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

Asked in: MHT CET Full Test 11

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