1. **Problem:** Given the premises $(A \lor C) \to \neg D$ and $A \lor C$, prove $\neg D$. 2. **Rule of inference:** This is an example of *Modus Ponens*, which states that if $p \to q$ and $p$ are both true, then $q$ must be true. 3. **Explanation:** - Premise 1: $(A \lor C) \to \neg D$ - Premise 2: $A \lor C$ - By Modus Ponens, since $(A \lor C)$ is true and it implies $\neg D$, we conclude $\neg D$. **Final answer:** The rule of inference used is **Modus Ponens**.