Find the subsets of the set with zero elements, one element, two elements, three elements, and four elements.
∅, { a}, { e}, { i}, { o}, { a, e }, { a, i }, { a, o }, { e, i }, { e, o }, { i, o }, { a, e, i}, { a, e, o}, { a, i, o}, { e, i, o}, { a, e, i, o}
Practice makes perfect
A subset of a set is also a set. The requirement is that all elements in the subset are also elements of the original 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 four elements in our original set. We can use each of these to form the single element subsets.
{a}, {e}, {i}, {o}
Two-Element Subsets
Next, we need to find all the two-element subsets.
{ a, e }, { a, i }, { a, o }, {e, i }, {e, o }, {i, o}
Three-Element Subsets
After that, we need to find all the three-element subsets.
{a, e, i }, {a, e, o }, {a, i, o }, {e, i, o }
Four-Element Subsets
The original set has four elements, so we can only form one subset having 4 elements: the original set itself.
{ a, e, i, o }
Summary
We have a total of 16 subsets.
∅, { a}, { e}, { i}, { o},
{ a, e }, { a, i }, { a, o }, { e, i }, { e, o }, { i, o },
{ a, e, i}, { a, e, o}, { a, i, o}, { e, i, o},
{ a, e, i, o}
