Union and Intersection Calculator

Union and Intersection of Sets

The union of sets contains every element that appears in at least one set. The intersection contains only elements common to all sets.

If A = {1, 2, 3, 4, 5} and B = {3, 6, 7, 2}, then A ∪ B = {1, 2, 3, 4, 5, 6, 7} and A ∩ B = {2, 3}.

What is the difference between union and intersection?

Union gathers elements from any set (at least one). Intersection keeps only elements present in every set (all of them).

Is the union commutative?

Yes. A ∪ B = B ∪ A and A ∩ B = B ∩ A. The order of sets does not change the result.

What is an empty intersection?

When sets share no common elements, the intersection is the empty set ∅. For example, {1, 2} ∩ {3, 4} = ∅.

Can I enter more than two sets?

Yes. This calculator supports two or three sets. Union and intersection extend naturally to three or more sets.