Set Builder Calculator

Your details

Enter elements separated by commas. Numbers and letters both work. Duplicates are removed automatically.
The second set. Used for all binary operations.
The universal set used when computing the complement of A or B. Must contain all elements of both sets for the complement to be meaningful.
Choose the set operation to perform. Complement requires a Universal Set. Power set grows as 2^n so is capped for large inputs.
Result
{1, 2, 3, 4, 5, 6, 7}

The computed set or answer in roster notation

|A| (cardinality of A)5
|B| (cardinality of B)5
|Result| (cardinality)7
A ⊆ BNo
B ⊆ ANo
A = BNo
|A|5
|B|5
|Result|7

Operation: Union (A ∪ B)

  • A and B share 3 elements in common: 3, 4, 5.
  • The result has 7 elements.
  • Set builder notation {x | condition} describes sets by a rule; roster notation lists the elements explicitly.

Next stepTry the symmetric difference to find elements unique to each set, or the power set to see all possible subsets.

 = Powered by OnlyCalculators