I've got these questions and I've given it some thought but I'm not how to move forward. The question is.

Let A and B be two sets. Prove the following propositions are logically equivalent.

a) B is a subset of A

b) A intersection of B = B

c) A union of B = A

I was thinking to convert this notation into proposition notation (and, or, not, etc..) and then use thruth tables to prove they are the same. The reason I cant move forward with this question this way is that I have no idea how set theory notation can be changed to proposition notation, or even it this is the right way to answer a question life this. Any help or resource you can point me to would be really great. thanks in advance.