Answer:
(a) 31
(b) 32
Step-by-step explanation:
We will do (b) first since it will help us do (a).
(b)
There are [tex]n(A)=5[/tex] elements in [tex]A[/tex]. Using the formula for the number of subsets of a given (finite) set, the number of subsets of [tex]A[/tex] is
[tex]2^{n(A)}=2^5=32[/tex]
(a)
A subset of [tex]A[/tex] is called proper if it does not equal [tex]A[/tex]. The only subset of [tex]A[/tex] that is not proper is [tex]A[/tex] itself, so simply subtract 1 from the number of subsets to get the number of proper subsets, which is
[tex]32-1=31[/tex]
