Which of these are simple and which are compound sentences?
She sings and dances.
He is rich yet humble.
John is a student, but Mike isn’t.
As we know, a compound sentence contains at least two independent clauses, and a simple sentence contains exactly one independent clause. None of the two contains any dependent clause.
With the definition out of the gate, let’s examine the three sentences. How many independent clauses each contains? Are the parts on either side of coordinating conjunctions (and, yet, and but, respectively) independent clauses?
She sings and dances.
He is rich yet humble.
John is a student, but Mike isn’t.
The first two underlined parts are clearly not independent clauses, but the third is. (Mike isn’t is elliptical form of Mike isn’t a student. In elliptical forms, we usually drop words that repeat. For example, in the last sentence, I didn’t write the third is an independent clause.)
The first two sentences contain exactly one independent clause, implying they’re simple sentences. The third contains two independent clauses, implying it’s a compound sentence.
She sings and dances. [One independent clause, with subject She and compound verb sings and dances]
He is rich yet humble. [One independent clause, with subject He and verb is. Note that rich yet humble is a compound adjective occupying the predicate position]
John is a student, but Mike isn’t. [Two independent clauses, with John and is and Mike and is as the two subject-verb units]
If he had written the first two sentences in the following manner, they would be compound. (Note the comma. Independent clauses are separated by a coordinating conjunction and a comma.)
She sings, and she dances. [Two independent clauses, with She and sings and she and dances as the two subject-verb units. Its earlier version had one subject-verb unit.]
He is rich, yet he is humble. [Two independent clauses, with He and is and he and is as the two subject-verb units. Its earlier version had one subject-verb unit.]
However, we avoid writing sentences like the above. To make sentences concise, we drop the common subject, reducing the number of independent clauses from two to one.