Prove $(\overline{A \cap B}) \subseteq \overline{A} \cap \overline{B}$.
But the same relation with a $=$ isn't always true. Can someone find an example where the $=$ doesn't hold, I can't seem to find one.
Thanks in advance.
2026-04-13 05:03:48.1776056628
counterexample for $\overline{A \cap B} = \overline{A} \cap \overline{B}$
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Let $A=(0,1)$ and $B=(1,2)$. Then $A\cap B=\emptyset$ so the LHS is empty. But the RHS equals $\{1\}$ since $\overline A=[0,1]$ and $\overline B=[1,2]$.