A subset of a set is also a set. The requirement is that all elements in the subset are also elements of the set. We can list all the subsets starting with the ones having zero elements, followed by one, two, and three elements.
Zero-Element Subsets
The only subset of any set with zero elements is the empty set. We write this using the empty set notation.
∅
One-Element Subsets
There are three elements in our original set. We can use each of these to form the single element subsets.
{ 0}, { 1}, { 2}
Two-Element Subsets
Next, we need to find all the two-element subsets.
{ 0, 1 }, { 0, 2 }, { 1, 2 }
Three-Element Subsets
The original set has three elements, so we can only form one subset having 3 elements: the original set itself.
{ 0, 1, 2 }
Summary
We have a total of eight subsets.
∅, { 0}, { 1}, { 2},
{ 0, 1 }, { 0, 2 }, { 1, 2 }, { 0, 1, 2 }
