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Set theory calculator

Compute every core set operation at once from two, three or four sets: union, intersection, both differences, symmetric difference, complement, Cartesian product and power set. It also checks subset, equality and disjointness, and reports all the cardinalities — numbers, letters or words all work.

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Set theory calculator works straight from this page — free, instant, nothing to install. It covers union, intersection, both differences, symmetric difference, complement, Cartesian product and power set. It also checks subset, equality and disjointness, and reports all the cardinalities — numbers, letters or words all work — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Set theory calculator do?

Compute every core set operation at once from two, three or four sets: union, intersection, both differences, symmetric difference, complement, Cartesian product and power set. It also checks subset, equality and disjointness, and reports all the cardinalities — numbers, letters or words all work.

What does a concrete case look like?

{1, 2, 3} ∪ {3, 4} = {1, 2, 3, 4} · ∩ = {3} · ∖ = {1, 2} — the tool shows every step in between, not just the final figure.

What does it take into account?

It factors in union, intersection, both differences, symmetric difference, complement, Cartesian product and power set. It also checks subset, equality and disjointness, and reports all the cardinalities — numbers, letters or words all work. Change any of them and the output follows immediately.

When would I actually use this?

Anything modelled as points and connections: a shortest route, a network's capacity, a schedule with dependencies, or a circuit reduced to its logic.

What is the most common mistake?

Assuming a shortest path stays shortest when a weight changes sign. Negative edges break the greedy argument Dijkstra rests on, and the algorithm returns a confident wrong answer rather than an error.

How is Set theory calculator different from Group theory order calculator?

They sit next to each other but answer different questions: Group theory order calculator is the one to open when you need it to analyse the classic finite groups — cyclic Zₙ, direct products Zₘ×Zₙ, dihedral Dₙ and symmetric Sₙ. It gives the group order, whether it is abelian, its structure, the number of generators for cyclic groups, and the order of any element you enter, including a permutation in cycle notation for Sₙ. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Julia set generator is the closest one after this: Render Julia sets in your browser by iterating z → z² + c for a fixed complex parameter c. Each pixel is a starting point coloured by how fast it escapes to infinity. Try famous values — the Douady rabbit, San Marco dragon, dendrite — tune the iterations and palette, and zoom in.

Where do the figures come from?

The algorithms are the textbook ones and their results are exact for the graph you enter. What varies is cost: several of these problems have no known efficient solution, so large inputs are answered by heuristic and the tool says when that is the case.

Further reading

All guides →
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Set theory calculator — OneKitly