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 four elements in our original set. We can use each of these to form the single element subsets.
{ +}, { -}, {*}, {÷}
Two-Element Subsets
Next, we need to find all the two-element subsets.
{ +, -}, { +, *}, { +, ÷}, { -, *}, { -, ÷}, {*, ÷}
Three-Element Subsets
After that, we need to find all the three-element subsets.
{ +, -, *}, { +, -, ÷}, { +, *, ÷}, { -, *, ÷}
Four-Element Subsets
The original set has four elements, so we can only form one subset having four elements: the original set itself.
{ +, -, *, ÷}
