A={1,2,3},B={1,2,2,3}. Is B⊆A? And is B⊂A? I was thinking yes to the first question and no to the second. They are equal sets right even though B has duplicate elements.

$$A=B$$
So yes to the first and no to the second.
Don't worry about the duplicates. When we're talking about sets, only the existence matter and not how many times. Sets that counts how many times it appears are referred as multisets.
