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 $X\cap {A}^{c}=\emptyset, \quad (A-B)\cup X=X?$

×