# Algebraic property of a set

If $$A$$ and $$B$$ are subsets of $$U=\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$$ such that ${ A }^{ c }\cap { B }^{ { c } }=\{1, 9\}, A\cap B =\{2\}, { A }^{ c }\cap B=\{4, 6, 8\},$ what is the set $$A?$$

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