Page 146 - Mathematics_Form_Two

Sets

Sets can be described in different ways. The repetition of elements has no effect,
most common ways of describing a set are: then the set of all letters in the word
by statement form, by listing (roster form), AGRICULTURE is:
and by a formula (set builder notation). For {A, C, E, G, I, L, R, T, U}
instance, if set A is a set of even numbers, (b) The word “DISTINGUISH” has the
then it can be described as follows: following distinct letters: D, I, S, T,
FOR ONLINE READING ONLY
(a) Statement from: A = {even numbers}
Mathematics for Secondary Schools (c) Using a formula: n =! } and is {D, I, S, T, N, G, U, H }.
N, G, U, and H. Therefore, the set of
(b) By listing: A={2, 4, 6, 8, 10, ...}
all letters in DISTINGUISH is:

2 , wheren
 :xx =
A =
1, 2, 3,...
n∈
(c) The word “EQUATION” has the
read as A is the set of all x such that x
vowels: A, E, I, O, and U. Therefore,
is an even number.
the set of all vowels in the world
EQUATION is:
Example 7�1
Given a set {A, E, I, O, U }
A = {odd numbers between 1 and 10}.
Describe the set A by; Exercise 7�1
(a) listing In questions 1 to 3, list the elements of
(b) set builder notation each of the following sets:
Solution 1. A = {x : x is an odd number less
(a) A = {3, 5, 7, 9} than 10}
=
(b) A = { :xx = 2n − , where n ∈ N 2. B {days of the week that begin
1
and 2 ≤ n ≤ 5}. with the letter S}
=
3. C {prime numbers less than 13}
Example 7�2

Describe the following sets in roster In questions 4 to 8, write each of the sets
form. in statement form:
(a) The set of all letters in the word 4. A = {1, 2, 3, 4, . . .}
“AGRICULTURE”. 5. B = {1, 3, 5, 7, 9, 11}
(b) The set of all letters in the word 6. C = {a, e}
“DISTINGUISH”. 7. C = {2, 3, 5, 7, 11, 13, 17, 19}
(c) The set of all vowels in the word
“EQUATION”. 8. E = {a, e, i, o, u}

Solution In questions 9 to 12, write each set using
(a) It is observed that the distinct letters
in the word “AGRICULTURE” are a set builder notation:
=
A, C, E, G, I, L, R, T, and U. Since 9. A {even numbers}
the order in which the elements are
=
written is does not matter and the 10. B {numbers divisible by 5}

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 140
MATHEMATIC F2 v5.indd 140 11/10/2024 20:13:11