Every pronoun must agree with its antecedent in person, number, and gender. Antecedent is the noun or other pronoun that a pronoun replaces or refers to. Third person is the category for whoever or whatever is spoken about or written about and is the classification for all nouns.
Number refers to the singular or plural nature of a word.
Antecedents joined by and usually require plural pronouns. Ann and Grace sold their books. The winner and the loser brought their trophies. Either the cows or the horse must move from its stall. Neither the horse nor the cows must move from their stalls.