Show that $A \cup B=A \cap B$ implies $A=B$.
Show that $A \cup B=A \cap B$ implies $A=B$.
Let $a \in A.$ Then $a \in A \cup$ $B$. Since $A \cup B=A \cap B, a \in A \cap B$.
So $a \in B$
Therefore, $A \subset$ $B.$ Similarly, if $b \in B$, then $b \in A \cup$ $B.$
Since $A \cup B=A \cap B, b \in A \cap B .$ So, $b \in A .$
Therefore, $B \subset A .$ Thus, $A=B$
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