\[ \sim S \vee (\sim R \wedge S) \] Step 1: Apply De Morgan's Law \[\] The negation of the entire expression \(\sim S \vee (\sim R \wedge S)\) is: \[ \sim (\sim S \vee (\sim R \wedge S)) \] According to De Morgan's law, the negation of a disjunction (OR) is the conjunction (AND) of the negations. So, we apply De Morgan's law to this: \[ \sim (\sim S) \wedge \sim (\sim R \wedge S) \] This simplifies to: \[ S \wedge \sim (\sim R \wedge S) \] Step 2: Apply De Morgan's Law Again \[\] Next, we need to negate the conjunction \(\sim R \wedge S\). By De Morgan's law, the negation of a conjunction is the disjunction of the negations: \[ \sim (\sim R \wedge S) = \sim \sim R \vee \sim S = R \vee \sim S \] Thus, the expression becomes: \[ S \wedge (R \vee \sim S) \] Step 3: Simplify the Expression \[\] Now, we distribute \(S\) over the disjunction \(R \vee \sim S\): \[ S \wedge (R \vee \sim S) = (S \wedge R) \vee (S \wedge \sim S) \] Since \(S \wedge \sim S\) is always false (a contradiction), we are left with: \[ S \wedge R \] Thus, the negation of \(\sim S \vee (\sim R \wedge S)\) is: \[ S \wedge R \]