How Many Subsets?

Consider the set S

1)  How many total subsets does S have?  A subset of S is a set A whose elements are all elements of S.

2)  How many subsets of S contain the element 4?

3)  How many subsets of S are of size 4?

4)  How many subsets of S contain only odd numbers?

As usual, try to come up with a few different ways to approach these problems.  What are some other interesting questions we could ask?


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