A set contains nine elements.
a) How many subsets does it have?
b) How many proper subsets does it have?
Step-1:Subsets:
Set is said to be a subset of Set if all the elements of Set are also present in Set . i.e. set is contained inside Set .
Types of Subsets
Step-2: Finding the number of subsets:
We know that, The number of elements in Set is .
Then the number of subsets formed by Set is .
Given, The number of elements in Set is .
Therefore, The number of subsets formed by Set is .
Step-3: Finding the number of proper subsets:
Set is considered to be a proper subset of Set if Set contains at least one element that is not present in Set .
We know that,
The number of elements in Set is .
Then the number of proper subsets formed by Set is .
Given, The number of elements in Set is .
Therefore, The number of proper subsets formed by Set is .
Hence, the number of subsets is and the number of subsets proper subsets is .