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 0 elements, followed by 1, 2, 3 and 4 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 4 elements in our original set. We can use each of these to form the single element subsets.
{ 1}, { 3}, { 5}, { 7}
Two-Elements Subsets
After that, we need to find all the two-elements subsets.
{ 1, 3}, { 1, 5}, { 1, 7},
{ 3, 5}, {3, 7}, {5, 7}
Three-Elements Subsets
Next, we need to find all the three-elements subsets.
{ 1, 3, 5}, { 1, 3, 7}, { 1, 5, 7}, {3, 5, 7}
Four-Elements Subsets
The original set has 4 elements, so we can only form one subset having 4 elements, the original set itself.
{ 1, 3, 5, 7 }
Summary
We have a total of 16 subsets.
∅, { 1}, { 3}, { 5}, { 7}, { 1, 3}, { 1, 5},
{ 1,7}, { 3,5}, { 3,7}, { 5,7}, { 1,3,5},
{ 1,3,7}, { 1,5,7}, { 3,5,7}, { 1,3,5,7}
