Lesson 9 of 1524
Sets
A set is a collection whose membership you can decide.
Practice this chapterRoster notation lists the members: {2, 4, 6}. Set-builder notation gives the rule instead. The empty set has no members, and its size is 0.
The union is “in either set.” The intersection is “in both.” If you add the two sizes, the overlap is counted twice, so you subtract it once.
Size of a union
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
Add the two sets, then remove the double-counted overlap.
Worked example
12 people are in A, 9 are in B, and 4 are in both. How many are in A or B?
- 1“A or B” is the union. Its size is n(A) + n(B) − n(A ∩ B).
- 2Add the two lists: 12 + 9 = 21. The 4 people who are in both were counted in the 12 and counted again in the 9.
- 3Subtract that overlap once: 21 − 4 = 17.
- 4Split it to see why. Only A: 12 − 4 = 8. Only B: 9 − 4 = 5. Both: 4. Then 8 + 5 + 4 = 17.
Result: 17
Why. Adding the sizes counts the overlap twice, so you subtract it once. The 17 people are everyone in at least one of the two sets.
The complement is everything in the universe that is outside the set. It depends on which universe you named.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.