Use De Morgan's laws to write the negation of the statement below Express the negation in a form such that the symbol $\sim$ negates only simple statements \[ \sim p \wedge(q \rightarrow \sim r) \] The negation of $\sim p \wedge(q \rightarrow \sim r)$ is $\square$

Step 1 ：De Morgan's laws state that the negation of a conjunction is the disjunction of the negations, and the negation of a disjunction is the conjunction of the negations. In other words, \( \sim (p \wedge q) = \sim p \vee \sim q \) and \( \sim (p \vee q) = \sim p \wedge \sim q \).

Step 2 ：In this case, we have a conjunction \( \sim p \wedge(q \rightarrow \sim r) \). So, we can apply De Morgan's law to get the negation of this statement.

Step 3 ：Also, we need to remember that the negation of an implication \( p \rightarrow q \) is \( p \wedge \sim q \).

Step 4 ：So, the negation of \( \sim p \wedge(q \rightarrow \sim r) \) is \( p \vee \sim (q \rightarrow \sim r) \), which simplifies to \( p \vee (q \wedge r) \).

Step 5 ：Final Answer: The negation of \( \sim p \wedge(q \rightarrow \sim r) \) is \( \boxed{p \vee (q \wedge r)} \).