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> Let $A, B$ be sets. Prove that $A \cap B = A$ iff $A \cup B = B$.
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My current progress:  

$\Rightarrow$:
Suppose $A \cap B = A$,
Let $x \in A$ be an arbitrary element.
Based on the above assumption, we have $x \in B$ and therefore $x \in A ∪ B$

Please advise on how to proceed. Thanks