1. **Problem:** Simplify the compound proposition $\neg (p \wedge q) \vee p$ using logical laws. 2. **Formula and rules:** Use De Morgan's Law: $\neg (p \wedge q) \equiv \neg p \vee \neg q$. 3. **Step-by-step solution:** 1. Start with the expression: $$\neg (p \wedge q) \vee p$$ 2. Apply De Morgan's Law to $\neg (p \wedge q)$: $$ (\neg p \vee \neg q) \vee p$$ 3. Use the associative and commutative laws of disjunction to regroup: $$ \neg p \vee (\neg q \vee p)$$ 4. By commutative law, $\neg q \vee p \equiv p \vee \neg q$: $$ \neg p \vee (p \vee \neg q)$$ 5. By associative law, this is: $$ (\neg p \vee p) \vee \neg q$$ 6. $\neg p \vee p$ is a tautology (always true), so: $$ \text{True} \vee \neg q$$ 7. By domination law, $\text{True} \vee \neg q \equiv \text{True}$. 4. **Final answer:** $$\neg (p \wedge q) \vee p \equiv \text{True}$$ This means the compound proposition is always true (a tautology).