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Description of a Set is taught in the note for Sets. Read it below and look for the section on this topic.

Sets

10 min read

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 .

Types of set
TypeMeaningExample
Empty set ∅no elementsmonths with 40 days
Finite setelements can be counted{a, e, i, o, u}
Infinite setnever ends{1, 2, 3, …}
Universal set ξeverything we are discussingall learners in a school
Subset
means every element of is also in . For example .

Operations on sets

The shaded region changes with each operation.
Venn diagrams for setsTwo overlapping circles inside a rectangle for the universal set, showing the regions A only, A and B together, and B only. A second Venn diagram with three overlapping circles A, B and C.A onlyA ∩ BB onlyUA ∪ B = everything inside both circlesA∩Ball 3ABCU
OperationSymbolMeaning
UnionA ∪ Bin A or B or both
IntersectionA ∩ Bin both A and B
ComplementA′in the universal set but not in A
Take away the overlap so it is not counted twice.
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?

  1. Learners playing at least one sport.
  2. Subtract from the whole group.

Answer: 2 learners play neither sport.

Check yourself A = {1, 2, 3, 4} and B = {3, 4, 5}. What is A ∩ B?
Check yourself n(A) = 10, n(B) = 12 and n(A ∩ B) = 4. What is n(A ∪ B)?

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.
Types of Sets