The negation of the logical statement $(\mathrm{p} \vee \sim \mathrm{q}) \rightarrow(\mathrm{p} \wedge \sim…

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

Solution

$\sim[p \vee \sim q \rightarrow(p \wedge \sim q)]$ $\equiv \sim \sim(p \vee \sim q) \vee(p \wedge \sim q)]$ $\equiv(p \vee \sim q) \wedge \sim(p \wedge \sim q)$ $\equiv(p \vee \sim q) \wedge(\sim p \vee q)$

Asked in: MHT CET 2020 (20 Oct Shift 1)

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