Answer:
The answer is indeed letter A. The king or the queen will bring his or her own personal servant.
Explanation:
Let's begin our analysis with the second sentence, letter B: "The king or the queen will bring his own personal servant." In this sentence, the possessive pronoun used, "his", makes it sound as if a servant belonging only to the king will be brought. The servant can be brought by any of them, the king or the queen, but belongs to the king.
Letter C is "The king or the queen will bring their own personal servant." By using the possessive "their", the speaker makes it sound as if the servant belongs to both of them, to the king and the queen at the same time.
Since we are looking for the sentence that uses the pronoun correctly to indicate that the king and the queen have separate servants, we should choose letter A. In "The king or the queen will bring his or her own personal servant", the use of both possessive pronouns "his" and "her" makes it clear that the king will bring the servant that belongs to him, while the queen will bring the servant that belongs to her.
