Topic: Affirmative Negative Agreement,

Best Answer Explained in Below-:

In the sentence "I can remember all their names and so ___ my sister," the correct word to complete the sentence is "can" (option A). This is because the sentence conveys a parallel or similar ability between the speaker and their sister. The structure "I can... and so can my sister" illustrates that both individuals possess the ability to remember names.

The choices "does," "might," and "may" do not fit the context as effectively. "Does" suggests a habitual action but does not align with the ability to remember names. "Might" and "may" imply a possibility rather than an ability, introducing uncertainty which does not match the affirmative statement being made.

Therefore, using "can" in this context clearly establishes that just as the speaker has the ability to remember names, the sister shares that same ability. This structure emphasizes a shared ability rather than an undefined action or possibility, making option A the logical and grammatically correct choice.