The task is to prove that $R \lor S$ follows logically from the given premises using rules of inference.

The premises provided are:

1. $C \lor D$
2. $(C \lor D) \to \neg H$
3. $\neg H \to (A \land \neg B)$
4. $(A \land \neg B) \to (R \lor S)$

Objective: Prove $R \lor S$.

Steps using rules of inference:

1. From Premise 1: $C \lor D$

2. From Premise 2: $(C \lor D) \to \neg H$ Using Modus Ponens on Premises 1 and 2, we can conclude: $\neg H$

3. From Premise 3: $\neg H \to (A \land \neg B)$ Using Modus Ponens on the result from step 2 and Premise 3, we conclude: $A \land \neg B$

4. From Premise 4: $(A \land \neg B) \to (R \lor S)$ Using Modus Ponens again on the result from step 3 and Premise 4, we conclude: $R \lor S$

Thus, we have successfully derived $R \lor S$ from the given premises using rules of inference like Modus Ponens.

Would you like more details on any specific inference step? Here are five additional related questions:

1. How does Modus Ponens work in logical derivations?
2. Can you explain how other rules like Modus Tollens might be applied in similar proofs?
3. What happens if one of the premises is false? Would the conclusion still hold?
4. How would the proof change if we had $\neg (C \lor D)$ instead of $C \lor D$?
5. Can we apply Disjunctive Syllogism here, and how does it differ from Modus Ponens?

Tip: When using Modus Ponens, always ensure you have both the implication and the truth of the antecedent to derive the consequent!