## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 5 Sets Check Your Progress

Question 1.

Write the following sets in tabular form and also in set builder form:

(i) The set of even integers which lie between -6 and 10.

(ii) The set of two digit numbers which are perfect square.

(iii) {factors of 42}

Solution:

(i) Given set = {-4, -2, 0, 2, 4, 6, 8)

(tabular form)

or {x : x = 2n, n ∈ I and -3 < n < 5}

(set builder form)

(ii) The set can be written as { 16, 25, 36, 49, 64, 81 } (tabular form)

or {x : x = n^{2}, n ∈ N and 4 ≤ n ≤ 9)

(set builder form)

(iii) The set can be written as { 1, 2, 3, 6, 7, 14, 21, 42) (tabular form)

or {x : x ¡s a factor of 42)

(set builder form)

Question 2.

Write the following sets in roster form:

(i) {x : x = 5n, n ∈ I and -3 < n ≤ 13}

(ii) {x : x = n^{2}, n ∈ W and n < 5}

(iii) {x : x = n^{2} – 2, n ∈ W and n < 4}

Solution:

The set can be written as

(i) Integers lie between -2 and 3 are -2, -1, 0, 1, 2, 3.

Given x = 5n, putting n = -2, -1,0, 1, 2, 3, we get

x = 5 × -2, 5 × -1, 5 × 0, 5 × 1, 5 × 2, 5 × 3,

= -10, -5, 0, 5, 10, 15

Set = {-10, -5, 0, 5, 10, 15)

(tabular form)

(ii) Whole numbers less than 5 are 0, 1, 2, 3, 4.

Given x = n^{2}, putting n 0, 1, 2, 3, 4, we get

x = 0^{2}, 1^{2}, 2^{2}, 3^{2}, 4^{2} = 0, 1, 4, 9, 16

Given set = {0, 1, 4, 9, 16) (roster form)

Whole numbers less than 4 are 0, 1, 2, 3

Given x = n^{2} – 2, putting n = 0, 1, 2, 3, We get

x = 0^{2} – 2, 1^{2} – 2, 2^{2} – 2, 3^{2} – 2

= -2, -1, 2, 7

Given set = {-2, -1, 2, 7}(roster form)

Question 3.

Write the following sets in set builder form:

(i) {-14, -7, 0, 7, 14, 21, 28}

(ii) {1, 2, 3, 6, 9, 18}

Solution:

(i) {x | x = 7n, n ∈ I and -2 ≤ n ≤ 4} (set builder form)

(ii) Given set = {x | x ∈ N, x is a factor of 18} (set builder form)

Question 4.

Classify the following sets into the finite set, infinite set the empty set. In the case of a (non-empty) finite set, mention the cardinal number.

(i) The set of even prime numbers.

(ii) {multiples of 9}

(iii) {x : x is a prime factor of 84}

(iv) {x : 2x + 5 = 1, x ∈ N}

(v) {x : x is a month of a year having less than 30 days}

(vi) {x | x is a month of a leap year having 28 days}

Solution:

(i) It is a finite set having 1 element. So, cardinal number = 1

(ii) It is an infinite set as it has the unlimited number of different elements.

Because, if we write it in roster form, the given set = {9, 18, 27, 36, ……….}

(iii) Prime factors of 84 = 2, 3, 7.

The set can be written as = {2, 3, 7}

It is a finite set having 3 elements.

(iv) 2x + 5 = 1

⇒ 2x = 1 – 5

⇒ 2x = -4

⇒ x = -2

But x ∈ N and Natural numbers are {1, 2, 3, …….}

It is an empty set.

(v) {x : x is a month of a year having less than 30 days}

= February

It is a finite set as it is one element.

(vi) {x | x is a month of a leap year having 28 days}

= Φ

It is an empty set as there is no month in the leap year which has 28 days.

Question 5.

In the following, determine whether A and B are equivalent sets and if so, whether A = B.

(i) A = {1, 3, 5}, B = {Red, Blue, Green}

(ii) A = {prime factors of 70}, B = {prime factors of 60}

(iii) A = {even natural numbers less than 10}, B = {odd natural numbers less than 10}

Solution:

(i) A ↔ B as n (A) = 3 = n (B)

But A ≠ B because, they have different elements.

(ii) Prime factors of 70 = 2, 5, 7

A = {2, 5, 7}

Prime factors of 60 = 2, 3, 5

B = {2, 3, 5}

A ↔ B as n (A) = n (B)

But A ≠ B

they have not the same elements.

(iii) If we write A and B in tabular form, we get

A = {2, 4, 6, 8}

B = {1, 3, 5, 7, 9}

So, n (A) ≠ n (B)

A is not equivalent to B.

Question 6.

Let P = {letters of SCHOOL} and Q = {letters of FALSE}, then State whether each of the following statement is true or false for the above sets:

(i) P ⊂ Q

(ii) Q ⊂ P

(iii) P ↔ Q

Solution:

If P = {letters of SCHOOL}

Q = {letters of FALSE}

P = {S, C, H, O, L} and Q = {F, A, L, S, E}

(i) P ⊂ Q – False.

(ii) Q ⊂ P – False.

(iii) P ↔ Q – True.

{Both have equal number of elements}

Question 7.

State whether each of the following statement is true or false for the sets A, B and C where

A = {x | x ∈ N, x < 40 and x is a multiple of 6}

B = {x | x ∈ W, x ≤ 40 and x is a multiple of 8}

C = {x | x is a factor of 28}.

(i) A ↔ B

(ii) B ↔ C

(iii) A ↔ C

Solution:

If we write A, B and C in tabular form, we get 32,

A = {6, 12, 18, 24, 30, 36},

B = {0, 8, 16, 24, 40}

and C = {1, 2, 4, 7, 14, 28}

(i) A ↔ B True, because n (A) = 6 = n (B)

(ii) B ↔ C True, because n (B) = 6 = n (C)

(iii) A ↔ C True, because n (A) = 6 = n (C)