Descriptions of Set Operations
In mathematics, a set operation is a function that takes two sets, or unordered lists, and generates a third list based on a standard operation. These operations are related to, but different from, stardard math operations like addition and subtraction in that they act on the entire list as a whole.
See below for a more detailed description of each operation.
Union
The union of two sets contains all the elements that appear in either of the sets. Another way of thinking about it is to imagine the union as the "sum" of the two sets, set 1 and set 2, excluding any duplicate values.
For example, suppose Mary and Carlos are buying fruits and vegetables at a farmstand. Mary's basket contains:
- berries,
- lettuce, and
- apples
and Carlos's basket contains:
- lettuce,
- peppers,
- onions, and
- berries
When they get home, together they purchased the following:
- apples,
- berries,
- lettuce,
- peppers, and
- onions
This is the union of the two sets!
Intersection
The intersection of two sets is only the elements that appear in both sets. The most common way to think about this is to visualize the intersecting part of a Venn Diagram. This is the list of items that are shared between the two sets.
For example, suppose you are a teacher and are trying to determine which of your students play multiple sports based on the roster of each team. The tennis team roster contains:
- Jason,
- James,
- Emily, and
- Robert
while the swim team roster includes:
- Emily,
- Jared,
- Larry, and
- Rachel
If you want to see which student is shared between the two sports, you determine that the only student that plays multiple sports is:
- Emily
This is the intersection of the two sets!
Difference
The difference of two sets is all the elements that appear in the first set, except for any elements that appear in the second set. Unlike union and intersection, order matters when determining the difference, as the second set is “subtracted” from the first set.
For example, suppose a teacher is trying to create a list of all their students that are in math courses except for any students that are currently taking geometry. She can use the difference of two sets to identify the list of students. The full list of students taking math courses is:
- Stacy,
- Matthew,
- Jon,
- Caroline
and the list of students taking geometry are:
- Stacy, and
- Matthew
Thus, the list of students she wants is:
- Caroline, and
- Jon
This is the difference of two sets!