A set contains nine elements.

a) How many subsets does it have?

b) How many proper subsets does it have?

a) The set has _ subsets. (Simplify your answer.)

a) The set has 512 subsets.

b) The set has 511 proper subsets.

Step-by-step explanation:

a) The set has 512 subsets.

Reason:

Number of all subsets of a set containing n elements is 2^n subsets,

Then the number of all subsets of a set containing 9 elements is:

2^n=2^9

=2*2*2*2*2*2*2*2*2

=512 subsets.

b) The set has 511 proper subsets.

Reason:

Number of proper subsets of a set containing n elements is 2^n-1 proper subsets,

Then the number of proper subsets of a set containing 9 elements is:

2^n - 1 = 2^9 - 1

=2*2*2*2*2*2*2*2*2 - 1

=512-1

=511 proper subsets ...