20. Neither the students nor the instructor knows where the notice is to be posted.
You are correct! There is nothing wrong with the sentence.
In this case, the singular verb, "knows," matches up with the immediately preceding singular subject, "instructor." If "students" and "instructor" were reversed, "students" would appear right before the verb. The verb would have to reflect the plural subject, "students." So the sentence would then read, "Neither the instructor nor the students know where the notice is to be posted."
You are correct! There is nothing wrong with the sentence.