11.1 Definition of Set
1. A set is a collection of objects according to certain characteristics
2. The objects in a set are known as elements.
3. Sets are usually denoted by capital letters and notation used for sets is braces, { }.
Example:
A = {1, 3, 5, 7, 9}
4. In set notation, the symbol
means ‘is an element of’ or ‘belongs to’ and
means ‘is not an element of’ or ‘does not belong to’.
Example 1:
Given that P= {factors of 15} and Q = {positive perfect squares less than 28}. By using the symbol
, complete each of the following:
(a) 5 ___ P (b) 20 ___ P (c) 25 ___ Q (d) 8 ___ Q
Solution:
P = {1, 3, 5, 15}, Q = {1, 4, 9, 16, 25}
(A) Determine whether a set is an empty set
5. A set with no elements is called an empty set or null set. The symbol φ or empty braces, { }, denotes empty set. For example, if set A is an empty set, then A = { } or A = φ and
n (A) = 0.
6. If B = {0} or {φ} does not denote that B is an empty set. B = {0} means that there is an element ‘0’ in set B.
B = {φ} means that there is an element ‘φ’ in set B.