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- #1

I have two small questions regarding operations on sets.

(1) Prove that \[A\subseteq B\subseteq C\] if and only if \[A\cup B=B\cap C\].

(2) What can you say about sets A and B if \[A\B = B\] ?

In the case of (1), I have used a Venn diagram and I understand why it is true, but struggle to prove it.

In the case of (2) I think it means that B is an empty set , am I correct ?

Thank you !