Page 105 - ICSE Math 6

Solution: (a) Odd natural numbers less than 9 are 1, 3, 5 and 7. Therefore, X = {1, 3, 5, 7}
(b) Consonants in the word ROSTER are R, S and T. Therefore, A = {R, S, T}
(c) Integers between –3 and 3 are –2, –1, 0, 1 and 2. Therefore, Y = {–2, –1, 0, 1, 2}

Example 4: Represent the following sets in the set-builder form.
(a) A = {2, 4, 6, 8, 10}
(b) X = {a, e, i, o, u}

(c) B = {January, March, May, July, August, October, December}
Solution: (a) A = {x | x is an even natural number less than 12}, or
A = {x | x is one of the first five multiples of 2}
(b) X = {x | x is a vowel in the English alphabet}
(c) B = {x | x is a month with 31 days}

Example 5: Write the following sets in the tabular form.
(a) A = {x | 2x + 2 = 0} (b) X = {x | 5x – 15 ≤ 0, x ∈ N}
Solution: (a) Consider, 2x + 2 = 0
⇒ 2x + 2 – 2 = 0 – 2 (Subtracting 2 from both the sides)
⇒ 2x = –2
2x –2
⇒ = (Dividing both the sides by 2)
2 2
⇒ x = –1
\ A = {–1}
(b) Consider, 5x – 15 ≤ 0
⇒ 5x – 15 + 15 ≤ 0 + 15 (Adding 15 on both the sides)
⇒ 5x ≤ 15
5x 15
⇒ 5 ≤ 5 (Dividing both the sides by 5)

⇒ x ≤ 3
\ x ≤ 3 and x ∈ N
Thus, X = {1, 2, 3}

Example 6: If X = {3, 5, 7, 9, 11}, write the roster form of set Y whose members are obtained by
adding 2 to the members of set X. Also, complete the set-builder form of set Y given
by Y = {y | y = x + ___, x ∈ ___ }.
Solution: The members of set Y are obtained by adding 2 to the members of set X. So,
Y = {5, 7, 9, 11, 13}
Also, Y = {y | y = x + 2, x ∈ X}

EXERCISE 7.1

1. Which of the following collections are sets?
(a) The collection of odd natural numbers less than 50.

(b) All the intelligent girls in your school.
(c) The collection of seven colours of a rainbow.

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