### Step 1: Introduction of the Concept A **Context-Free Grammar (CFG)** is a formal system that describes the structure of a language using rules (productions). The given CFG is: **S → aS | ba** This means we can replace S with either "aS" or "ba", generating strings by applying these rules recursively. --- ### Step 2: Correct Answer and Explanation **Correct Answer:** **c. All words with an arbitrary number of a's followed by ba** **Explanation:** Let's analyze the production: - Start with S. - If we keep applying S → aS, we get strings like aS, aaS, aaaS, etc. - Eventually, we must use S → ba to stop the recursion, giving us strings like: - ba - aba - aaba - aaaba - ... and so on. So, the language consists of any number (including zero) of 'a's followed by "ba". --- ### Step 3: Why Other Options Are Not Correct - **a. All words with the substring ab:** The grammar does not guarantee the presence of "ab" as a substring. It only guarantees a string of 'a's followed by "ba". - **b. All words that start with an a:** The string "ba" is also generated, which does not start with 'a'. - **d. All words with an arbitrary number of as followed by ab:** The grammar specifically ends with "ba", not "ab". **Final Answer: c** --- ### Summary Sentence - **Step 1:** We introduced context-free grammars and the given production. - **Step 2:** We identified the correct answer and explained why. - **Step 3:** We eliminated incorrect options and justified our choice.