Defining a Set – Elements of a Set

A set is a group of items (in most cases) of the same kind. The items in a set are called the elements or members of a set. A set is well-defined when all its members can be listed.

Examples of well-defined sets

1. A = the set of even numbers between 1 and 15
= {even numbers between 1 and 15}
= {2, 4, 6, 8, 10, 12, 14}

2. B = the set of multiples of 5 between 8 and 28
= {multiples of 5 between 8 and 28}
= {10, 15, 20, 25}

Note:
1. a set may be denoted by a capital letter (as shown above)
2. {} means ‘the set of’

Example of elements of a set

From example 1 above,

A = {2, 4, 6, 8, 10, 12, 14}
Therefore: 2, 4, 6, 8, 10, 12, 14 are all elements of set A.
That is: 2, 4, 6, 8, 10, 12, 14 Є A (Where the symbol Є means ‘is an element of’).

The number of elements in set A is 7.
That is, n(A) = 7
Where n(A) means ‘the number of elements in set A’.