Answer: |A|+|B|+|C|-|A∩B|-|A∩C|-|B∩C|+|A∩B∩C|.
- A |A|+|B|+|C|, leaving out all the overlaps between the sets
- B |A|+|B|+|C|-|A∩B|-|A∩C|-|B∩C|+|A∩B∩C|
- C |A|+|B|+|C|-|A∩B∩C|, subtracting just the triple overlap once
- D |A∩B∩C|, taken as if it represented the entire union
Correct answer: B. |A|+|B|+|C|-|A∩B|-|A∩C|-|B∩C|+|A∩B∩C|
Explanation: Add singles, subtract pairwise intersections (over-subtracted), add back triple (under-subtracted). |A∪B∪C| = |A|+|B|+|C| − |A∩B| − |A∩C| − |B∩C| + |A∩B∩C|.
Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.
Concept context
Counting, arrangements, and selections