Math

Union and Intersection Calculator

Find |A ∪ B| from the sizes of two sets and their intersection.

Calculated Output

|A ∪ B| 17

Only in A 8

Only in B 5

Formula: |A ∪ B| = |A| + |B| − |A ∩ B|

Step-by-Step Breakdown

1. Values used:

2. |A| (size of A) = 12

3. |B| (size of B) = 9

4. |A ∩ B| (overlap) = 4

6. |A ∪ B| = 17

7. Only in A = 8

8. Only in B = 5

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The math behind it

|A ∪ B| = |A| + |B| − |A ∩ B|. Subtracting the intersection removes the elements counted twice.

|A| = 12, |B| = 9, overlap = 4 → union = 12 + 9 − 4 = 17.

What if the sets are disjoint?

Then |A ∩ B| = 0 and the union is simply |A| + |B|.