The semicolon links up two related ideas by narrowing the gap between the ideas of two separate sentences or independent clause by replacing a conjunction between two related ideas. The group of words that comes before the semicolon should form a complete sentence, the group of words that comes after the semicolon should form a complete sentence, and the two sentences should share a close, logical connection. After semicolon you can/t use capital letters.
According to the definition given, the choice that shows the proper way to join two independent clauses with a semicolon is:
Michelle’s birthstone is a diamond; Debra’s is an opal. (two independent clauses)
The other options do not apply because:
My birthstone is a ruby; not a diamond. (They are not two independent clauses)
Diamonds are popular; My birthstone is a ruby. (the second clause begins with a capital letter).
Michelle’s birthstone is a diamond; but Debra’s is an opal. (The two sentences are connected with a connector but).