Question

Let A = {3, 4, 5, 6, 7, 9, 10, 11}

a. How many subsets does A​ have?

b. How many proper subsets does A​ have?

(Type a whole number)

Answer 1

a. 256

b. 255

Explanation:

If a set has “n” elements, then the number of subset of the given set is
`2^n` and number of proper subset is
`2^n-1`

A = {3, 4, 5, 6, 7, 9, 10, 11}

Here, n = 8

No of subsets

`= {2}^(n) = {2}^(8) = 256`

No of proper subsets

=
`2^n-1 = 256-1=255`