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j = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(a) P = {1, 4, 9}
Thus, P9 = {2, 3, 5, 6, 7, 8, 10}
(b) Q = {1, 2, 5, 10}
Thus, Q9 = {3, 4, 6, 7, 8, 9}
Self Practice 11.2a
1. Identify whether each of the following is the universal set of {1, 3, 5, 7, 9, 11, 13, 15}:
(a) {whole numbers}
(b) {prime numbers}
(c) {x : x is a positive integer and x < 15}
2. Given that j = {whole numbers which are less than 10}, determine the complement
of each of the following sets:
(a) P = {multiples of 3}
(b) Q = {prime numbers}
LEARNING
STANDARDS
How do you represent the universal set and Represent
complement of a set by using Venn diagram? (i) the relation of a set
and universal set, and
Besides description and set notation, a set can also be (ii) complement of a set
represented by an enclosed geometrical diagram which is through Venn diagrams.
known as Venn diagram.
For example,
j = {Amir, Hazura, Laila, Sandra, Zamri, Dali, Pei San, Yana}
A = {Amir, Hazura, Laila, Sandra, Zamri} • A set can be represented
by a circle, an oval, a
A9 = {Dali, Pei San, Yana} rectangle or a triangle. CHAPTER
• The universal set is
The relationship between the sets above can be represented commonly represented
by the following Venn diagram. by a rectangle. 11
Universal set, ξ is represented ξ A
by a rectangle. Amir Set A is represented by
Dali a circle.
Hazura
Each dot represents an element. Laila
Sandra All the elements of set A
Zamri are written in the circle.
Elements of complement of Pei San
set A lie outside the circle. Yana
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Introduction of Set