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Empty set
Think Smart
State the month There is no
with 32 days. month with How many months have
32 days! 28 days?

id ou now
If M represents the set of month with 32 days, then set M • An empty set is also
does not contain any element and is known as an empty set. called a null set.
An empty set can be represented with the symbol f or { }. • The symbol f is read
as phi.
Thus, M = f or M = { }.

Self Practice 11.1b

1. Describe each of the following sets by using (i) description, (ii) listing and
(iii) set builder notation.
(a) Colours of the rainbow (b) Multiples of 3 which are less than 25
2. Determine whether each of the following statements is TRUE or FALSE.
(a) If P = {triangles which have diagonals}, then P = f.
(b) If Q = {prime numbers which are also even numbers}, then Q = { }.
(c) If R = {odd numbers which are divisible by 2}, then R = f.
3
(d) If S = {x : x is a negative integer and x , 0}, then S = { }.
What is the element of a set?
LEARNING
The elements of a set are defined according to certain STANDARDS
characteristics. Each of the elements must satisfy the Identify whether an object
CHAPTER
11 conditions of the set that is defined. is an element of a set and
represent the relation
For example, set A = {local fruits in Malaysia}. using symbol.

Durian is a local fruit, so durian is an element of set A.
Symbol  is used to represent ‘is an element of’ the set.
Therefore, durian  A.

Apple is not a local fruit, so apple is not an element of now
set A. Symbol  is used to represent ‘is not an element of’ id ou
the set. Symbol  is called
epsilon.
Therefore, apple  A.

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Chapter 11