Use this **calculator** to calculate the *union*, *intersection*, or *difference* between two sets. Start by **copy-pasting** your two sets into the text boxes Data Set #1 and Data Set #2. Then, choose the operation to perform. The result will be displayed in the Output.

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Use commas, spaces, or new lines to separate each item in your sets. Choose your output format by adjusting the checkboxes underneath the output.

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.

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!

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,
- Emily, and
- Robert

while the swim team roster includes:

- Emily,
- 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!

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!