Solve the Following Questions


The proposition $\mathrm{p} \rightarrow \sim(\mathrm{p} \wedge \sim \mathrm{q})$ is equivalent to:

  1. $(\sim \mathrm{p}) \vee \mathrm{q}$

  2. q

  3. $(\sim \mathrm{p}) \wedge \mathrm{q}$

  4. $(\sim p) \vee(\sim q)$

Correct Option: 1


$\mathrm{p} \rightarrow \sim(\mathrm{p} \wedge \sim \mathrm{q})$

$=\sim p \vee \sim(p \wedge \sim q)$

$=\sim p \vee \sim p \vee q$

$=\sim(p \wedge q) \vee q$

$=\sim p \vee q$

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