If , , and is the set of all integers, then the number of subsets of the set is .

Question

If , ,  and  is the set of all integers, then the number of subsets of the set  is .

Canvas Classes · Accepted Answer

🧠 Build , ,  One at a Time, Then Intersect, Then Complement

The expression  looks heavy, but it is just a sequence of three clean steps. Do them one at a time and do not try to compute the complement first.

The smart order is: build , ,  as intervals, then intersect (the intersection is usually a small union of intervals), then take complement (one more flip), then intersect with  (now you just count integers in a bounded interval). Finally apply the formula: a set with  elements has  subsets

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