The negation of the statement

Question:

The negation of the statement

$\sim p \wedge(p \vee q)$ is :

  1. (1) $\sim p \wedge q$

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

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

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

Correct Option: , 4

Solution:

$\therefore \sim p \wedge(p \vee q) \equiv \mathrm{p} \vee \sim \mathrm{q}$

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