Is os Are?

Teachers aren't 100% perfect, and that's why we prep for class. I hardly disagree with the answer key, but this one sounds wrong to me. Edit: Typo in my title.

Which is correct?:

"A set of twins that is not identical is called fraternal."

"A set of twins that are not identical are called fraternal."

The second sounds better. I'm talking about the individuals in the pair and not as one unit.

It does say " A set of..." which technically means the verb should be singular. Regardless, it sounds wrongs to me. What do you think? If you have nothing but negativity to contribute, keep it yourself.