A compound subject is a subject made up of two or more simple subjects. The simple subjects can be nouns, noun phrases, noun clauses or pronouns.
In a compound subject, the simple subjects are joined by coordinating or correlative conjunctions. "And" is an example of coordinating conjunction, and "neither...nor" is an example of two correlative conjunctions that work together.
Because compound subjects have two or more parts, they mostly take a plural verb. However, there are exceptions.
When the conjunction "and" combines the elements of the compound subject, the verb is normally plural. Some examples include "My brother and his sister are married to each other" and "Running and doing yoga are my two favourite ways to work out." However, when the elements add up to the same idea, the verb is singular. One example is: "The wear and tear on the car was tremendous." Another exception is when the second element is superfluous and can be omitted, like in this sentence: "Anyone who has read the book and anybody who has even heard of its ideas agrees with the author."
When the conjunction "or" or "nor" combines the elements of the compound subject, the verb is often singular because the elements are not considered as a group. If the two elements are both singular, the verb is singular. If the parts are plural, the verb must be plural. If the compound subject contains both plural and singular nouns, the verb must agree with the noun that is nearest to it.