Pronouns must match the words to which they refer—also known as their antecedents. This is what we call ‘pronoun agreement.’
The antecedent is the noun or group of words to which the pronoun is referring The pronoun and its antecedent must agree in number, gender, and person.
Examples for ‘number’:
The antecedents (Brad, Bill) are joined by ‘nor,’ which means that because you have two singular antecedents joined by ‘nor,’ you must choose a singular pronoun—his.
The antecedents (Tom, John) are joined by ‘and,’ which means that because you have added two singular antecedents together, you have a plural, so the pronoun must be plural—their.
Pronoun agreement for ‘gender’ means that you must be consistent in the use of the gender of the pronoun (neuter, masculine, or feminine).
Pronoun agreement for ‘person’ means that if you are speaking of a singular item, use a singular pronoun. Singular pronouns are I, me, my, he, him, his, she, her, hers, it, and its. Plural pronouns are you, we, us, they, them, our, their.
Correct: Each company had its own rules. Our company had our own rules.