Final answer:
The correct grammar for the sentence "The dog and the cat are playing" is "B. The dog and the cat are playing".
Step-by-step explanation:
The correct grammar for the sentence "The dog and the cat are playing" is B. The dog and the cat are playing. When two subjects are joined by "and", they form a compound subject and the verb should be in the plural form. In this sentence, "dog" and "cat" are the two subjects, so the correct verb form is "are".