Definition of Sets

A set is a collection of objects, things or symbols which are clearly defined.

The individual objects in a set are called the members or elements of the set.

A set must be properly defined so that we can find out whether an object is a member of the set.

There are two ways of doing this.

1. Listing the elements

The set can be defined by listing all its elements, separated by commas and enclosed within braces.

Example:
B = {2, 4, 6, 8, 10}
X = {a, b, c, d, e}

However, in some instances, it is impossible to list all the elements of a set. In such cases, we define the set by method 2.

2. Describing the elements

The set can be defined, where possible, by describing the elements.

Example:
C = {x : x is an integer, x > – 3 }
This is read as: “C is the set of elements x such that x is an integer greater than –3.”

D= {x: x is a river in a river}

We should describe a certain property which all the elements x, in a set, have in common so that we can know whether a particular thing belongs to the set.

We relate a member and a set using the symbol ∈. If an object x is an element of set A, we write x ∈ A. If an object z is not an element of set A, we write z ∉ A.

∈ denotes “is an element of’ or “is a member of” or “belongs to”

∉ denotes “is not an element of” or “is not a member of” or “does not belong to”

Example:
If A = {1, 3, 5} then 1 ∈ A and 2 ∉ A

This video introduces the basic vocabulary used in set theory.

This video defines and give the notation used for subsets and proper subsets.

This video introduces Venn diagrams and set operations.

Custom Search

Useful Links:
Sets