Venn diagrams
- A Venn diagram sorts things into overlapping circles inside a rectangle. The rectangle is the universal set, ξ: everything being considered.
- The overlap holds things in both sets. Things in neither set go inside the rectangle but outside the circles.
Set notation
- 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.
- If ξ = {1, 2, …, 10}, A = even numbers and B = multiples of 3, then A ∩ B = {6} and A ∪ B = {2, 3, 4, 6, 8, 9, 10}.
Filling in a Venn diagram
- Start with the overlap, then work outwards. Don't forget the region outside the circles.
- In a class of 30, 18 play football, 12 play tennis and 5 play both. Football only = 13, tennis only = 7, and 30 − 25 = 5 play neither.
Probabilities from Venn diagrams
- Divide the number in the region you want by the total number in ξ.
- In the class above, P(plays exactly one sport) = (13 + 7) ÷ 30 = 20/30 = 2/3.
Key terms
- Set
- A collection of things, such as numbers, written in curly brackets.
- Element
- One member of a set.
- Universal set (ξ)
- Everything being considered.
- Intersection (A ∩ B)
- The elements in both A and B.
- Union (A ∪ B)
- The elements in A or B or both.
- Complement (A′)
- The elements not in A.