Page 153 - Mathematics_Form_Two

Sets

Complement of a set Number of elements in a set
If A is a subset of a universal set, then The number of elements in a finite set is
the complement of set A is the set that found by counting each element in the set.
contains all the elements that are in the The number of elements in a set is also
universal set but not in A. It is denoted by known as the cardinality of the set. For

c
A or A . For instance, if U = {a, b, c, example, you might want to find the number
FOR ONLINE READING ONLY
d, ..., z} and A = {a, b}, then of elements in the union, intersection, or
A′ = {c, d, e, ..., z}. complements of finite sets. If the set is
infinity, then its cardinality is infinities.
Example 7�11 Engage in Activity 7.3 to explore how to

Given = {15, 45, 135, 275} and determine the number of elements in a set. Mathematics for Secondary Schools
A = {15}, find A′.
Activity 7�3: Exploring the number
Solution of elements in a set
A′ = {45, 135, 275} 1. Consider the universal set
µ = { :xx ≤ 10, x∈  },
Example 7�12 A = { is a prime numberx }, and
Given  = {a, e, i, o, u}and B = { is an odd numberx }.
B = {e, i}, find Bʹ. List all the elements of ,µ A, B,

B
A ∩ B, A ∪ , A ∩ B, ′ A ∪ B,
Solution and A′∩ B.
The set B′ contains all elements which 2. Explore different sources such as
are not in B. offline and online libraries to learn
how to find the number of elements
Therefore, B′ = {a, o, u}. in a set.
3. Use the knowledge acquired in task
Example 7�13 2 to find the number of elements of
sets in task 1.
Given  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 4. Study the number of elements of
11, 12, 13, 14}, the sets A, B, A ∩ B, and A ∪
B
A = {2, 3, 5, 7, 11, 13}, and in task 3, then deduce any unique
relationship.
=
B {2, 4, 6, 8, 10, 12, 14}, find: 5. Study the number of elements in ,µ
(a) A′∪B′ (b) A∩B′ A, and A′ and deduce any unique
Solution relationship.
From the given sets, it implies that, 6. State the number of elements of
A′∩
B, A ∩
B, and A, and A, and deduce

A′ = {1, 4, 6, 8, 9, 10, 12, 14} any relationship between the number
B′ = {1, 3, 5, 7, 9, 11, 13}. of elements of the sets.
(a) A′∪B′= {1, 3, 4, 5, 6, 7, 8, 9, 10, 7. Based on your observations in tasks
11, 12, 13, 14} 4 to 6, write mathematical statements
to generalize your findings and share
(b) A∩B′ = {3, 5, 7, 11, 13} with others.

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 147
11/10/2024 20:13:18