Which of the following sentences uses the correct form of the verb?

The sentence "She doesn't like running." is correct because it properly uses the negative contraction "doesn't," which stands for "does not." In English grammar, when forming negative sentences in the present simple tense with third-person singular subjects (he, she, it), the auxiliary verb "does" is used, followed by "not" (contracted to "doesn't") and then the base form of the main verb, which in this case is "like."

Using "doesn't" correctly indicates that the subject, "she," does not enjoy the action of running. The base form of the verb "like" must remain unchanged after the auxiliary "does," making this structure grammatically accurate.

In other options, incorrect forms of "do" or mismatched verb conjugations lead to errors. Therefore, “She doesn't like running.” is the only grammatically correct choice among the options.