Agreement

The rules of grammar require writers to make sure that verbs agree in number with their subjects.

To my compatriots, I have no hesitation in saying that each one of us is as intimately attached to the soil of this beautiful country as are the famous jacaranda trees or Pretoria and the mimosa trees of the bushveld.
—from "Glory and Hope" written by South African leader Nelson Mandela

The sentence uses both a singular and a plural verb (in red) to agree in number with each subject (in blue).

Subject and Verb Agreement

Subjects and verbs must agree in number. A singular subject must have a singular verb, and a plural subject must have a plural verb. A phrase or clause that interrupts a subject and its verb does not affect subject-verb agreement.
Singular – A box of cookies is in the cabinet.
Plural – Two boxes of spaghetti are on the third shelf.

A compound subject joined by and is generally plural and must have a plural verb unless the subjects are thought of as one thing or modified by every or each.
Ian and Pete are on the same team.
Every boy and girl is expected to attend the assembly.

Two or more singular subjects joined by or or nor must have a singular verb. Two or more plural subjects joined by or or nor must have a plural verb.
Ed, Sue, or Pam has a good chance of winning the election.
Neither cars nor bicycles are allowed on this road.

If a singular subject is joined to a plural subject by or or nor, the subject closer to the verb determines whether the verb is singular or plural.
Either the employees or the owner shows visitors around. (Singular subject is closer to verb.)
Either the owner or the employees show visitors around. (Plural subject is closer to verb.)

Singular indefinite pronouns take singular verbs. Plural indefinite pronouns take plural verbs.
Singular – Each of the books is available in the library.
Plural – Both of the books are on the shelf.

A noun expressing an amount or a measurement is usually singular and requires a singular verb.
Two weeks is never enough vacation.
Three cups of sugar is a lot for that recipe.

A title or name of an organization is singular and must have a singular verb.
Hard Times is a novel by Charles Dickens.

Pronoun and Antecedent Agreement

A personal pronoun must agree with its antecedent in number, person, and gender.
My uncle likes his new job.
The cat has its own basket.
Alicia says this is hers.

Use a singular personal pronoun with two or more singular antecedents joined by or or nor. Use a plural personal pronoun with two or more antecedents joined by and.
Dawn or Sue will give you her notes.
Ed, Jon, and Bob brought their gloves.

When the gender of the antecedent is not specified, use his or her or rewrite the sentence so that a plural pronoun will be appropriate.
A student should keep his or her password a secret.
Students should keep their passwords a secret.

Use a singular personal pronoun to refer to a singular indefinite pronoun. Use a plural personal pronoun to refer to a plural indefinite pronoun.
Each of the girls has her own room.
Both of the boys rode their bikes.

A personal pronoun should always refer to a single, clear, and logical antecedent.
Poor – They make a lot of mistakes in that paper.
Better – That paper contains many factual errors.
Unclear – Bruce told Danny that his mother was sick.
Clear – Bruce told Danny that Bruce's mother was sick.