Compound sentences are sentences that consist of two or more independent clauses connected by a comma and coordinating conjunction or by a semicolon.
An independent clause is a clause that can stand alone as a sentence. Every sentence must contain a subject and predicate and express a complete thought. Independent clauses fulfill these criteria.
The given sentence consists of two independent clauses connected by a semicolon:
<em>We should go out to eat; </em>
<em>birthdays are special occasions.</em>
As we can see, both of these clauses make sense if they stand alone. This leads us to the conclusion that they are independent clauses that make up a compound sentence.