Question

Let the set A be defined as follows.

Answer 1

Answer:

(a) 31

(b) 32

Step-by-step 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

$32-1=31$