When a Pronoun has two or more antecedents connected by and, it must agree with them jointly in the plural, because they are taken together.
RULE XIII.—PRONOUNS.
When a Pronoun has two or more antecedents connected by or or nor, it must agree with them singly, and not as if taken together.
RULE XIV.—FINITE VERBS.
Every finite Verb must agree with its subject, or nominative, in person and number.
RULE XV.—FINITE VERBS.
When the nominative is a collective noun conveying the idea of plurality, the Verb must agree with it in the plural number.
RULE XVI.—FINITE VERBS.
When a Verb has two or more nominatives connected by and, it must agree with them jointly in the plural, because they are taken together.