How many elements are in the union of three disjoint sets with 36, 24, and 12 elements?

Question

Let |A| = 36, |B| = 24, |C| = 12, with the sets pairwise disjoint:

A ∩ B = A ∩ C = B ∩ C = ∅.

Find |A ∪ B ∪ C|.

Answer choices

1. 12
2. 72
3. 50
4. 24

Explanation

For pairwise disjoint finite sets, the size of the union is the sum of their sizes: no element is counted twice.

|A ∪ B ∪ C| = |A| + |B| + |C| = 36 + 24 + 12 = 72.

All intersection corrections in the inclusion–exclusion formula are zero in this case.