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.