🔵Set Operations Calculator

Calculate union, intersection, and difference of two sets.

Set A

|A| = 5 elements

Set B

|B| = 5 elements

A ∪ B — Union

All elements in A or B

{ 1, 2, 3, 4, 5, 6, 7 }

|result| = 7

A ∩ B — Intersection

Elements in both A and B

{ 3, 4, 5 }

|result| = 3

A − B — Difference

Elements in A but not B

{ 1, 2 }

|result| = 2

B − A — Difference

Elements in B but not A

{ 6, 7 }

|result| = 2

A △ B — Symmetric Difference

Elements in A or B but not both

{ 1, 2, 6, 7 }

|result| = 4

About Set Operations Calculator

Perform fundamental set theory operations — union, intersection, difference, and complement — on any two sets of numbers or values. The set operations calculator shows the result of each operation with a visual Venn diagram, making abstract set theory concepts concrete and easy to understand for students and educators.

How to Use Set Operations Calculator

1
Step 1
Enter Set A elements separated by spaces or commas (e.g., 1 2 3 4 5).
2
Step 2
Enter Set B elements in the same way.
3
Step 3
View the results of union, intersection, difference, and symmetric difference operations, along with the Venn diagram visualization.

Common Use Cases

Learning set theory concepts in discrete mathematics or computer science courses
Verifying set operation results during homework and problem sets
Understanding SQL JOIN operations by mapping them to set theory
Teaching Venn diagrams and set relationships in middle and high school math

Frequently Asked Questions

What set operations does the calculator support?

The calculator supports Union (A ∪ B), Intersection (A ∩ B), Difference (A − B and B − A), Symmetric Difference (A △ B), and displays the Venn diagram for each result.

Can I use non-numeric values in my sets?

Yes. Sets can contain any space-separated values including letters, words, or numbers. The tool treats each space-separated token as a set element.

What is a set in mathematics?

A set is a collection of distinct, unordered elements. Set theory is foundational to mathematics, logic, computer science, and database operations.