Set Operations Calculator

Calculate union, intersection, difference, symmetric difference, and Cartesian-product size for two finite sets.

Discrete MathSetsComputer Science Math

Calculate

Set A
Set B
Please enter valid values.

What this calculator teaches

Sets are collections of distinct elements. Set operations are the foundation of discrete mathematics, database logic, probability, and computer science.

This calculator treats repeated items as one set element and trims extra spaces.

Formula & Symbols

ConceptFormulaMeaning
UnionA ∪ BEverything in A or B.
IntersectionA ∩ BOnly elements in both A and B.
DifferenceA − BElements in A that are not in B.
Symmetric differenceA △ BElements in exactly one set.

Step-by-Step Examples

Example 1
Two number sets
  • A = {1,2,3,4}.
  • B = {3,4,5,6}.
  • Union combines all unique elements.
  • Intersection keeps only shared elements.
✓ A∪B={1,2,3,4,5,6}; A∩B={3,4}.

Where students use this

🎓
High school and college
Use the tool to check homework and understand each step.
📊
Data and modeling
Connect formulas to tables, graphs, and real values.
🧪
Science and engineering
Use math results inside physics, chemistry, and engineering problems.
💻
Computer science
Apply the same logic to algorithms, systems, and numerical work.

Common Mistakes to Avoid

⚠️
Counting duplicates

Sets contain distinct elements, so duplicates do not change the set.

⚠️
Confusing union and intersection

Union means OR; intersection means AND.

⚠️
Forgetting order does not matter

{1,2} and {2,1} are the same set.

Frequently Asked Questions

What is a set? ▾
A set is a collection of distinct objects called elements.
What is union? ▾
The union contains elements that are in A, in B, or in both.
What is intersection? ▾
The intersection contains only elements shared by both sets.
What is Cartesian product size? ▾
If A has m elements and B has n elements, A×B has m·n ordered pairs.

Related Math Calculators

🔢 Probability Calculator🔢 Combinations Calculator🔢 Permutations Calculator🔢 Modular Inverse and Extended Euclidean Calculator

Formula Explorer connections

Interpretation: This relationship converts, summarizes or checks numerical quantities using standard arithmetic and measurement rules. Assumption: Use consistent units, preserve enough significant digits, and round only the final result unless the method states otherwise.

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