When is A ∩ B^c = ∅ equivalent to A ∪ B^c = U?

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Does anyone know if this is true [itex]A \bigcap B^{c} = \emptyset \Leftrightarrow A \bigcup B^{c} = U[/itex] ?
 

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It's obviously false. You should readily be able to find a counter example even for U being a set of cardinality 3.
 

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