Set theory/Characterization of inclusion/Exercise

Let ${}A$ and ${}B$ be sets. Show that the following facts are equivalent.

1. ${}A\subseteq B$,
2. ${}A\cap B=A$
3. ${}A\cup B=B$,
4. ${}A\setminus B=\emptyset$,
5. There exists a set ${}C$ such that ${}B=A\cup C$,
6. There exists a set ${}D$ such that ${}A=B\cap D$.

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