ML Aggarwal Sets Check Your Progress Class 7 ICSE Maths Solutions

ML Aggarwal Check Your Progress Class 7 ICSE Maths Solutions. We Provide Step by Step Answer of Check Your Progress Questions for Sets as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-7.

ML Aggarwal Sets Check Your Progress Class 7 Maths Solutions

Board	ICSE
Publications	Avichal Publishig Company (APC)
Subject	Maths
Class	7th
Chapter-5	Sets
Writer	ML Aggarwal
Book Name	Understanding
Topics	Solution of Check Your Progress Questions
Edition	2023-2024

Sets Check Your Progress

ML Aggarwal Class 7 ICSE Maths Solutions

Page-115

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}

Answer:

(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 = n²
, n ∈ N and 4 ≤ n ≤ 9 )
(iii) the set can be written as { 1,2,3,6,7,14,21,42) ( tabular form )
Or { x:x is 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 = n², n ∈ W and n < 5}
(iii) {x : x = n² – 2, n ∈ W and n < 4}

Answer:

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× 1 , 5 × 2, 5 × 3,
= -10, -5, 0, 5, 10, 15
Set = { -10, -5, 0 ,5, 10, 15 }

(ii) whole numbers less than 5 are 0 ,1,2,3,4
Given x = n², putting n 0, 1,2,3,4 we get
X = 0², 1², 2², 3², 4² = 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 = n²-2 putting n = 0, 1, 2, 3, we get
X = 0²– 2, 1²-2, 2²-2, 3²-2
= -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}

Answer:

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

Answer:

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

(ii) It is an infinite set as it has 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.

(ML Aggarwal Sets Check Your Progress Class 7 ICSE Maths Solutions )

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}

Answer:

(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)

Question -6. 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