In a sentence, the subject agrees with its verb. A singular verb is used with a singular subject. A plural verb is used with a plural subject
EXAMPLE: A dog barks / Dogs bark.

If two subjects are joined by and, the verb must be in the plural.
EXAMPLE: My father and brother are going to Japan next month.

If two subjects are joined by or, either ... or, neither ... nor, the verb agrees with the subject nearest to it.
EXAMPLE: Either this book or those books are his.
EXAMPLE: Either they or he is responsible.
EXAMPLE: Neither you nor your friend is invited.
EXAMPLE: Neither the son nor the daughters are interested.