What is a set?
A set is a collection of things, called elements or members. We write sets in curly brackets: . We write to say 4 belongs to , and to say 5 does not. The number of elements is written , so .
| Type | Meaning | Example |
|---|---|---|
| Empty set ∅ | no elements | months with 40 days |
| Finite set | elements can be counted | {a, e, i, o, u} |
| Infinite set | never ends | {1, 2, 3, …} |
| Universal set ξ | everything we are discussing | all learners in a school |
- Subset
- means every element of is also in . For example .
Operations on sets
| Operation | Symbol | Meaning |
|---|---|---|
| Union | A ∪ B | in A or B or both |
| Intersection | A ∩ B | in both A and B |
| Complement | A′ | in the universal set but not in A |
Try itTwo overlapping sets
In a class of learners, set A studies Kiswahili and set B studies French. Change the numbers and see the regions. The numbers in the circles count the learners in each region.
Worked exampleA survey
In a group of 30 learners, 18 play football, 15 play netball and 5 play both. How many play neither?
- Learners playing at least one sport.
- Subtract from the whole group.
Answer: 2 learners play neither sport.
Key terms
- Element
- A member of a set.
- Union
- All elements that are in A or in B.
- Intersection
- Elements that are in both sets.
- Complement
- Elements of the universal set not in the set.
- Venn diagram
- A picture of sets using overlapping circles.
Summary
- A set is a collection written in { }; n(A) counts its elements.
- Union ∪: in either. Intersection ∩: in both. Complement ′: not in the set.
- n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
- Venn diagrams show the regions and help with counting.