Question

Let the set A be defined as follows.

A={h,m,s,d,c}
(a) Find the total number of proper subsets of A.


(b) Find the total number of subsets of A.

Answer 1

(a) 31

(b) 32

Explanation:

We will do (b) first since it will help us do (a).

(b)

There are
`n(A)=5` elements in
`A`. Using the formula for the number of subsets of a given (finite) set, the number of subsets of
`A` is

`2^(n(A))=2^5=32`

(a)

A subset of
`A` is called proper if it does not equal
`A`. The only subset of
`A` that is not proper is
`A` itself, so simply subtract 1 from the number of subsets to get the number of proper subsets, which is

`32-1=31`