These are distinct Subsets

Question

What is The number of distinct subsets of {2,3,4,...,21}

What is The number of distinct subsets of {3,4,5,...,16}

Answer 1

If a set A has n (distinct) elements then the number of all subsets of A is 2ⁿ

Answer 2

The number of distinct subsets is found by first figuring out the number of elements in the set then raising 2 to that number. In the first case, there are 20 elements in the set so the number of distinct subsets is 2²⁰. Plugging that in a calulator gives 1,048,576 distinct sets.

For the second problem, there are 14 elements in the set, so the number of distinct subsets is 2¹⁴ = 16,384 distinct subsets.