Union and Intersection Calculator

The union of two sets (A∪B) contains all elements that appear in either set A, set B, or both. The intersection (A∩B) contains only the elements that appear in both set A and set B simultaneously. In short, union is 'in any', while intersection is 'in all'.

To find the union, combine all elements from both sets and remove duplicates. To find the intersection, list only the elements that appear in both sets. For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A∪B = {1, 2, 3, 4} and A∩B = {2, 3}.

For intervals, the union covers the combined range of both intervals, while the intersection covers only the overlapping range. For example, [1, 5]∪[3, 8] = [1, 8] and [1, 5]∩[3, 8] = [3, 5]. This calculator works with discrete element sets, not continuous intervals.

Yes, both operations are commutative. This means A∪B = B∪A and A∩B = B∩A. The order in which you list the sets does not affect the result of a union or intersection.

Yes, both operations are distributive over each other. Specifically, A∪(B∩C) = (A∪B)∩(A∪C) and A∩(B∪C) = (A∩B)∪(A∩C). These are key properties used in set algebra and Boolean logic.

The set difference A − B (also written A \ B) contains all elements that are in set A but not in set B. For example, if A = {1, 2, 3, 4} and B = {3, 4, 5}, then A − B = {1, 2}.

Yes — sets can technically contain any distinct elements: numbers, letters, words, etc. This calculator accepts any comma-separated values, so you can enter letters or words as well as numbers and it will compute union and intersection correctly.

When two sets share no common elements, their intersection is the empty set (∅), which contains zero elements. Such sets are called disjoint sets. For example, {1, 2, 3} and {4, 5, 6} are disjoint because they share no elements.