Number of Sets

Algebra Level 2

Consider the following subsets of the integers: \[A=\{1, 2, 3, 4, 5, 6\} \mbox{ and } B=\{4, 5, 6, 7, 8\}. \] How many subsets \(X\) of integers satisfy \[ X\cap {A}^{c}=\emptyset, \quad (A-B)\cup X=X?\]

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