PEAZIT Aha card
Go straight to resources ↓Do not count the overlap of two sets twice
Adding the sizes of A and B counts their intersection twice. Subtract it once. Union means A or B, including both.
| Relation | Meaning |
|---|---|
| |A ∪ B| = |A| + |B| − |A ∩ B| | Add both lists and subtract the overlap. |
| |A| = 12; |B| = 9; |A ∩ B| = 4 | Four names occur on both lists. |
| |A ∪ B| = 12 + 9 − 4 = 17 | 17 different students play at least one sport. |
One worked example
- |A ∪ B| = |A| + |B| − |A ∩ B|Add both lists and subtract the overlap.
- |A| = 12; |B| = 9; |A ∩ B| = 4Four names occur on both lists.
- |A ∪ B| = 12 + 9 − 4 = 1717 different students play at least one sport.
Watch out: At least one includes both. Exactly one excludes the intersection.
Goal, prerequisites and card origin
What you will learn: Count elements belonging to at least one of two sets.
What you need first: Addition and the meaning of both.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Adding the sizes of A and B counts their intersection twice. Subtract it once. Union means A or B, including both.