Page 75 - ICSE Math 8

Here, letters A and L are being repeated so they are written only once.

Set-builder or rule form
In this form, we write a common property or a rule describing the elements. For example, the set of integers
between –3 and 5 can be written as:
A = {x : x is an integer, –3 < x < 5} or A = {x | x is an integer, –3 < x < 5}

A set written in roster form can be expressed in set-builder form and vice versa.

Example 2: Write the following sets in set-builder form.
(a) A = {2, 3, 5, 7, 11} (b) B = {a, e, i, o, u}
Solution: (a) A = {x : x is a prime number, x < 12} (b) B = {x : x is a vowel of English alphabet}
Example 3: Write the following sets in roster form.
(a) X = {x : x is a natural number, x < 15} (b) Y = {x : x is a letter of the word GREATER}
Solution: (a) X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} (b) Y = {G, R, E, A, T}

 1 23 4 5
Example 4: Write the set B =  ,, ,,  in set-builder form.
 3 4 5 6 7 
n
Solution: B = {x : x = , n ∈ N, 1 ≤ n ≤ 5}
n + 2

EXERCISE 6.1

1. Give two examples of a collection which are not sets.
2. Let K = {–4, –3, –2, –1, 0, 1, 2, 3, 4, 5}. Put the correct symbol of ∈ or ∉ in the blank spaces.
(a) –2 _____ K (b) 3 _____ K (c) –5 _____ K (d) 0 _____ K (e) 7 _____ K
3. Write the following sets in roster form.
(a) A = {x : x is a whole number, x ≤ 7} (b) B = {x : x = 2n + 1, n ∈ N, n < 4}
(c) C = {x : x is a 2-digit natural number such that the sum of its digits is 9}
(d) D = {x : x is a prime number which is a divisor of 30}

(e) E = {x : x is a letter of the word MATHEMATICS}
4. Write the following sets in set-builder form.
(a) P = {January, June, July} (b) S = {1, 4, 9, 16, 25, 36, 49} (c) T = {1, 3, 5, 7, 9, ...}
 1 11 1 1 
(d) U = 1,,, , ,  (e) V = {7, 14, 21, 28, 35, 42}

 2 4 8 16 32 
Types of Sets

In this section, you will study different types of sets with examples.

Finite set
A set with finite, i.e., countable number of elements is called a finite set. For example, if A = {x : x is a student
of class VIII of a particular school} and B = {x : x is a month of a year}, then A and B are finite sets.

Infinite set
A set in which we cannot count the number of elements present, i.e., uncountable number of elements is called an
infinite set. For example, if X = {x : x is a star in the sky} and Y = {1, 3, 5, 7, 9, 11,...}, then X and Y are infinite sets.

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