Union & Intersection Calculator

Calculate the union and intersection of 2 or 3 sets with detailed breakdown.

Input Sets

|A| = 4

|B| = 4

Exclusive Elements

Only in A:{1, 2}
Only in B:{5, 6}

Results

Union (A ∪ B)

{1, 2, 3, 4, 5, 6}

|Union| = 6

Intersection (A ∩ B)

{3, 4}

|Intersection| = 2

Pairwise Intersections

AB:

{3, 4}

Inclusion-Exclusion Verification

Calculated |Union|: 6

Actual |Union|: 6

Verified!

Formulas

Two Sets

|A ∪ B| = |A| + |B| - |A ∩ B|

Three Sets

|A ∪ B ∪ C| = |A| + |B| + |C| - |A∩B| - |A∩C| - |B∩C| + |A∩B∩C|