EXAMPLE 1.1.5
Let U = {1, 2, 3, 4, 5, 6, 7,...}
Let S = {x|x is less than 10}
1. How many subsets does S have?
2. How many proper subsets does S have?
SOLUTIONS
1. First note that S = {1, 2, 3, 4, 5, 6, 7, 8, 9}.
Since S has 9 elements, the number of subsets is
S has 512 subsets.
2. Since S has 512 subsets, it has 511 proper subsets.