Set notation is a short way to describe regions of a Venn diagram. A ∩ B (A intersection B) means in both A and B. A ∪ B (A union B) means in A or B or both. A′ means not in A.
To find n(A ∩ B) from totals, use the fact that n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Then probabilities follow, for example P(A ∪ B) = n(A ∪ B) ÷ total.
Worked example
There are 30 students. 18 like A, 15 like B and 8 like both. How many like neither?
- n(A ∪ B) = 18 + 15 − 8 = 25.
- Neither = 30 − 25 = 5.
Answer:5 students
Key words
- intersection (∩)
- in both sets
- union (∪)
- in either set
- complement (′)
- not in the set
Practise this
New questions every time.
Common Core-referenced: HSS-CP.A.1