ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 5 Sets Ex 5.1
Question 1.
State which of the following collections are set:
(i) All states of India.
(ii) Four cities of India having more than one lac population.
(iii) All tall students of your school.
(iv) Four colours of a rainbow.
(v) All the beautiful flowers.
(vi) All clever people of Lucknow.
(vii) Last three days of a week.
(viii)All months of a year having at least 30 days.
Solution:
(i) It is a set.
(ii) It is not a set because the collection is not well defined.
(iii) It is not a set because the collection is not well defined.
(iv) It is not a set because the collection is not well defined.
(v) It is not a set because the collection is not well defined.
(vi) It is not a set because the collection is not well defined.
(vii) It is a set.
(viii) It is a set.
Question 2.
Let A = {vowels of English alphabet}, then which of the following statements are true. In case a statement is incorrect, mention why.
(i) c ∈ A
(ii) {a} ∈ A
(iii) a, i, u, ∈A
(iv) {a, u} ∉ A
(v) {a, i, u } ∈ A
(vi) a, b, ∈ A
Solution:
(i) This statement is false because c is not a vowel.
(ii) This statement is false because {a} is a set and not an element.
(iii) This statement is true.
(iv) This statement is true.
(v) This statement is false because {a, i, u} is a set and not an element.
(vi) This statement is false because b is not a vowel, so b ∉ A., Of course, a ∈ A.
Question 3.
Describe the following sets:
(i) {a, b, c, d, e, f}
(ii) {2, 3, 5, 7, 11, 13, 17, 19}
(iii) {Friday, Saturday, Sunday}
(iv) {April, August, October}
Solution:
The given set can be written as
(i) The set of first six letters of alphabet, or {first six letters of alphabet}.
(ii) {prime numbers less than 20}
(iii) {last three days of a week}
(iv) {months of a year whose name begin with a vowel}
Question 4.
Write the following sets in tabular form and also in set builder form:
(i) The set of even whole numbers which lie between 10 and 50.
(ii) {months of a year having more than 30 days}
(iii) The set of single-digit whole numbers which are a perfect square.
(iv) The set of factors of 36.
Sol. The given set can be written as
(i) {12, 14, 16, 18, 20, ……. , 48} (tabular form)
{x : x = 2n, n ∈ N and 5 < n < 25} (set builder form)
(ii) {January, March, May, July, August, October, December) (Tabular form)
{x | x is a month of a year having 31 days} (set builder form)
(iii) {0, 1, 4, 9} (tabular form)
{x | x is a perfect square of one digit number) (set builder form)
(iv) {1,2, 3, 4, 6, 9, 12, 18, 36} (tabular form)
{x | x is a factor of 36} (set builder form)
Question 5.
Write the following sets in roster form and also in description form:
(i) {x | x = 4n, n ∈ W and n < 5}
(ii) {x : x = n2, n ∈ N and n < 8}
(iii) y : y = 2x – 1, x ∈ W and x < 5}
(iv) {x : x is a letter in word ULTIMATUM}
Solution:
(i) Whole numbers less than 5 are 0, 1, 2, 3, 4.
4n i.e., four times the above numbers are 0, 4, 8, 12, 16.
The given set can be written as {0, 4, 8, 12, 16} (roster form)
or
{whole numbers which are divisible by 4 and less than 20} (description form)
(ii) Natural numbers less than 8 are 1, 2, 3, 4, 5, 6, 7
n2 i.e., squares of these numbers are 1, 4, 9, 16, 25, 36, 49
The given set can be written as {1,4, 9, 16, 25, 36, 49} (roster form)
Or {squares of first seven natural numbers} (description form)
(iii) Whole numbers less than 5 are 0, 1, 2, 3, 4.
i.e. x = 0, 1, 2, 3, 4.
Given y = 2x – 1, putting x = 0, 1, 2, 3, 4, we get
y = 2 × 0 – 1, 2 × 1 – 1, 2 × 2 – 1, 2 × 3 – 1, 2 × 4 – 1
= 0 – 1, 2 – 1, 4 – 1, 6 – 1, 8 – 1
= -1, 1, 3, 5, 7
The given set can be written as {- 1, 1, 3, 5, 7} (roster form)
or
{odd integers which lie between -2 and 8} (description form)
(iv) The given set can be written as { U, L, T, I, M, A}(roster form)
[Write each element of the set once and only once]
or
(letters in the word ULTIMATUM}
(description form)
Question 6.
Write the following sets in roster form:
(i) {x | x ∈ N, 5 ≤ x < 10 }
(ii) {x | x = 6 p, p ∈ I and – 2 ≤ p ≤ 2}
(iii) {x | x = n2 – 1, n ∈ N and n < 5}
(iv) {x | x – 1 = 0}
(v) {x | x is a consonant in word NOTATION}
(vi) {x | x is a digit in the numeral 11056771}
Solution:
The given set can be written as
(i) {5, 6, 7, 8, 9} (roster form)
(ii) Integers lie between -2 and 2 are -2, -1, 0, 1, 2, or p = -2, -1, 0, 1, 2
Given x = 6p i.e. puttingp = -2, -1, 0, 1, 2,
we get x = 6 × (-2), 6 × (-1), 6 × 0, 6 × 1, 6 × 2
= -12, -6, 0, 6, 12.
The given set can be written as {-12, -6, 0, 6, 12} (roster form)
(iii) Natural numbers less than 5 are 1, 2, 3, 4
i.e., n = 1, 2, 3, 4
Given x = n2 – 1, putting n = 1, 2, 3, 4, we get
x = 12 – 1, 22 – 1, 32 – 1, 42 – 1 = 0, 3, 8, 15
The given set can be written as {0, 3, 8, 15} (roster form)
(iv) The given set can be written as {1}
(roster form)
x – 1 = 0 ⇒ x = 1
(v) The given set can be written as {N, T} (roster form)
(vi) The given set can be written as
{1, 0, 5, 6, 7} (roster form)
Question 7.
Write the following sets in set builder form:
(i) (1, 3, 5, 7, …….. 29}
(ii) {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}
(iii) {1, 4, 9, 16, 25, ………}
(iv) {\(\frac { 1 }{ 5 }\), \(\frac { 1 }{ 6 }\), \(\frac { 1 }{ 7 }\), …… \(\frac { 1 }{ 20 }\)}
(v) {-16, -8, 0, 8, 16, 24, 32, 40}
(vi) {January, June, July}
Sol.
The given set can be written as
(i) {x : x is an odd natural number, x < 30}
(ii) {x | x is a prime number, x < 30}
(iii) The given numbers are perfect squares of natural numbers
Given set = {x | x = n2, n ∈ N}
(iv) Given set = {x | x = \(\frac { 1 }{ n }\), n ∈ N and 5 ≤ n ≤ 20}
(v) The given numbers are multiples of 8 lying between -16 and 40.
Given set = {x | x = 8p, p ∈ I and -2 ≤ p ≤ 5}
(vi) Given set = {x : x is a month of a year whose name begins with letter ‘J’}
Question 8.
If V is the set of vowels in the word COMPETITION, write the given set in
(i) description form
(ii) set builder form
(iii) roster form
Solution:
V = {a set of vowels in the word COMPEITION} = {C, O, M, P, E, T, I, N}
(i) V = {Vowels in the word COMPETITION}
(ii) V = {x | x is a vowel in the word COMPETITION}
(iii) V = {O, E, I}