I have the following question:

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> Let $X$ be a topological space and let $A,B \subseteq X$ such that ${\left( {\bar A} \right)^{\text{o}}} = \emptyset = {B^{\text{o}}}$. Show that ${\left( {A \cup B} \right)^{\text{o}}} = \emptyset$.
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 Am I allowed to say that the empty set is a subset of every set so $\emptyset \subseteq {\left( {A \cup B} \right)^{\text{o}}}$?

 I'm struggling with the reverse inclusion: I have the following $ {\left( {A \cup B} \right)^{\text{o}}} \subseteq A \cup B \subseteq \overline {A \cup B} = \bar A \cup \bar B\ $, but I'm not sure where to go from there?