ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on sets Venn Diagrams Check Your Progress

Question 1.
If ξ={x : x ϵ N, r < 25} and A = {x : x is a composite number}, then find A’ in set builder from and also in roster form.
Solution:

Question 2.
If ξ = {x | x ϵ I, -5 ≤ x ≤ 5}, A = {-5, -3, 0, 3, 5} and B = {-4, -2, 0, 2, 4}, then
(i) Find A ∪ B and A ∩ B
(ii) Verify that n(A ∪ B) = n(A) + n(B) – n(A ∩ B).
(iii) Find A’ and verify that n(A) + n(A’) = n(ξ).
(iv) Find B’ and verify that n(B’) = n(ξ) – n(B)
(v) Find A ∪ A’, A ∩ A’, B ∪ B’ and B ∩ B’.
(vi) Find (A ∪ B)’ and A’ ∩ B’. Are they equal ?
(vii) Find (A ∩ B)’ and A’ ∪ B’. Are they equal ?
Solution:

Question 3.
If ξ = {x | x ϵ N, x ≤ 12}, A = {prime numbers} and B = {odd numbers}, then
(i) Find A ∪ B and A ∩ B.
(ii) Verify that n(A ∪ B) + n(A ∩ B) = n(A) + n(B).
(iii) Find A’ and B’.
(iv) Find (A ∪ B)’ and verify that n(A ∪ B) + n(A ∪ B)’ = n(ξ).
(v) Find (A ∩ B)’ and A’ ∪ B’. Are they equal ?
Solution:

Question 4.
If ξ = {x : x ϵ N, x ≤ 12}, A= {x : x ≥ 7} and B = {x : 4 < x < 10}. Find :
(i) A’
(ii) B’
(iii) A ∪ B
(iv) A ∩ B
(v) A – B
(vi) B – A
(vii) (A ∪ B)’
(viii) A’ ∩ B’
Also verify that:
(i) (A ∪ B)’ = A’ ∩ B’
(ii) A – B = A ∩ B’
(iii) n(A ∪ B) + n((A ∪ B)’) = n(ξ)
(iv) n(A ∪ B) = n(A – B) + n(B – A) + n(A ∩ B).
Solution:

Question 5.
Given A = {students who like cricket} and B = {students who like tennis}; n(A) = 20, n(B) = 15 and n(A ∩ B)= 5.
Illustrate this through a Venn diagram. Hence find n(A ∪ B).
Solution:

Question 6.
If n(ξ) = 50, n(A) = 15, n(B) = 13 and n(A ∩ B) = 10. Find n(A’), n(B’) and n(A ∪ B).
Solution:

Question 7.
If n(ξ) = 60, n(A) = 35, n(B’) = 36 and n((A ∩ B)’) = 51, find :
(i) n(B)
(ii) n(A ∩ B)
(iii) n(A ∪ B)
(iv) n(A – B)
Solution:

Question 8.
In a city, 50% of people read newspaper A, 45% read newspaper B, and 25% read neither A nor B. What percentage of people read both the newspapers A as well as B?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on sets Venn Diagrams Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) If A, B are two sets, then A ∪ B = …………..
(ii) If A, B are two sets, then A ∩ B = …………..
(iii) If A, B are two sets, then A – B = …………..
(iv) A and B are disjoint sets if and only if A ∩ B = …………..
(v) A and B are overlapping sets if and only if A ∩ B = …………..
(vi) The set {x: x ϵ W, x < 3} in the roster form = …………..
(vii) If A is any set, then A ∪ ϕ = and A ∪ ξ = …………..
(viii) If ξ = {all digits in our number system] and A ={1,2, 3, 4, 5}, then A’= …………..
(ix) If A is any set and A’ is its complement, then A ∪ A’ = and A ∩ A’ = …………..
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) If ξ is the universal set and A is any set, then A’ = {x; x ϵ ξ and r ∉ A}.
(ii) If A = {0,1,2,3,4, 5} and B = {0,3, 5, 7}, then A ∩ B = B.
(in) If A= {0,1, 2,3,4, 5} and B = {0,3,5,7}, then A ∪ B=A.
(iv) If ξ = {all digits in our number system}, A = {multiples of 2} and B = {multiples of 3}, then A ∩ B = {6}.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 12):
Question 3.
If A = {x | x is a colour of rainbow} and B = {white, red, green}, then A ∩ B is
(a) B
(b) {green}
(c) {red}
(d) {green, red}
Solution:

Question 4.
If P = {-1, 0, 1, 2, 5} and Q = {3, 5, 7}, then P ∪ Q is
(a) {5}
(b) {-1, 0, 1, 2, 3, 7}
(c) {-1, 0, 1, 2, 3, 5, 7}
(d) none of these
Solution:

Question 5.
If A and B are two sets, then A – B is defined as
(a) {x |x ϵ A or x ϵ B}
(b) {x | x ϵ A and x ϵ B}
(c) {x | x ϵ A and x ∉ B}
(d) {x | x ϵ B and x ∉ A}
Solution:

Question 6.
If A is any set, then A ∪ ϕ is
(a) A
(b) ϕ
(c) 2,
(d) none of these
Solution:

Question 7.
A ∩ ξ is same as
(a) A
(b) ϕ
(c) A’
(d) ξ
Solution:

Question 8.
If ξ = W and A = {x | x ϵ W and x ≤ 10}, then A’ is
(a) ϕ
(b) {x | x ϵ W and 0 ≤ x ≤ 10}
(c) {x | x ϵ W and x ≤ 10}
(d) {x | x ϵ W and x ≥ 11}
Solution:

Question 9.
If ξ= {x | x ϵ W, x ≤ 12}, A – {x | x is a multiple of 3} and B = {x | x is a multiple of 4}, then A ∩ B is
(a) ϕ
(b) {0}
(c) {12}
(d) {0, 12}
Solution:

Question 10.
If ξ = (all digits in our number system}, A = {x | x is prime} and B = {x | x is even}, then B – A is
(a) {4, 6, 8}
(b) {0, 4, 6, 8}
(c) {3, 5, 7}
(d) {2}
Solution:

Question 11.
If A and B are two sets such that n(A) = 22, n(B) = 18 and n(A ∪ B) = 35, then n(A ∩ B)
(a) 4
(b) 5
(c) 15
(d) 75
Solution:

Question 12.
In a town of 840 persons, 450 persons read Hindi, 300 read English and 200 read both. Then the number of person who read neither is
(a) 180
(b) 210
(c) 260
(d) 290
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on Sets Venn Diagrams Ex 6.2

Question 1.
From the adjoining Venn diagram, find the following sets :
(i) A
(ii) B
(iii) ξ
(iv) A’
(v) B’
(vi) A ∪ B
(vii) A ∩ B
(viii) (A ∪ B)’
(ix) (A ∩ B)’

Solution:

Question 2.
From the adjoining Venn diagram, find the following sets :

(i) P
(ii) Q
(iii) ξ
(iv) P’
(v) Q’
(vi) P ∪ Q
(vii) P ∩ Q
(viii) (P ∪ Q)’
(ix) (P ∩ Q)’
Solution:

Question 3.
From the adjoining Venn diagram, find the following sets :
(i) ξ
(ii) A ∩ B
(iii) A ∩ B ∩ C
(iv) C’
(v) A – C
(vi) B – C
(vii) C – B
(viii) (A ∪ B)’
(ix) (A ∪ B ∪ C)’

Solution:

Question 4.
Draw Venn diagrams to show the relationship between the following pairs of sets :
(i) A = {x | x ϵ N, x = 2n, n ≤ 5} and
B = {x | x ϵ W, x = 4n, n < 5}
(ii) A = {prime factors of 42} and
B = {prime factors of 60}
(iii) P = {x | x ϵ W, x < 10} and
Q = {prime factors of 210}
Solution:

Question 5.
Draw a Venn diagram to illustrate the following information:
n (A) = 22, n (B) = 18 and n (A ∩ B) = 5.
Hence find:
(i) n (A ∩ B)
(ii) n (A – B)
(iii) n (B – A)
Solution:

Question 6.
Draw a Venn diagram to illustrate the following information: n (A) = 25, n (B) = 16, n (A ∩ B) = 6 and n ((A ∪ B)’) = 5
Hence find:
(i) n (A ∪ B)
(ii) n (ξ)
(iii) n (A – B)
(iv) n (B – A)
Solution:

Question 7.
Given n(ξ) = 25, n (A’) = 7, n (B) = 10 and B ⊂ A. Draw a Venn diagram to illustrate this information. Hence, find the cardinal number of the set A – B.
Solution:

Question 8.
In a group of 50 boys, 20 play only cricket, 12 play only football and 5 boys play both the games. Draw a Venn diagram and find the number of boys who play
(i) at least one of the two games cricket or football.
(ii) neither cricket nor football.
Solution:

Question 9.
In a group of 40 students, 26 students like orange but not banana, while 32 students like orange. If all the students like atleast one of the two fruits, find the number of students who like
(i) both orange and banana
(ii) only banana.
Draw a Venn diagram to represent the data.
Solution:

Question 10.
In a group of 60 persons, 45 speak Bengali, 28 speak English and all the persons speak atleast one language. Find how many people speak both Bengali and English. Draw a Venn diagram.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 6 Operation on sets Venn Diagrams Ex 6.1

Question 1.
If A = {0, 1, 2, 3, …….., 8}, B = {3, 5, 7, 9, 11} and C = {0, 5, 10, 20}, find
(i) A ∪ B
(ii) A ∪ C
(iii) B ∪ C
(iv) A ∩ B
(v) A ∩ C
(vi) B ∩ C
Also find the cardinal number of the sets B ∪ C, A ∪ B, A ∩ C and B ∩ C.
Solution:

Question 2.
Find A’ when
(i) A= {0, 1, 4, 7} and E, = {x | x ϵ W, x ≤ 10}
(ii) A = {consonants} and ξ = {alphabets of English}
(iii) A = boys in class VIII of all schools in Bengaluru} and ξ = {students in class VIII of all schools in Bengaluru}
(iv) A = {letters of KALKA} and ξ = {letters of KOLKATA}
(v) A = {odd natural numbers} and ξ = {whole numbers}.
Solution:

Question 3.
If A {x : x ϵ N and 3 < x < 1} and B = {x : x ϵ Wand x ≤ 4}, find
(i) A ∪ B
(ii) A ∩ B
(iii) A – B
(iv) B – A
Solution:

Question 4.
If P = {x : x ϵ W and x < 6} and Q = {x : x ϵ N and 4 ≤ x ≤ 9}, find
(i) P ∪ Q
(ii) P ∩ Q
(iii) P – Q
(iv) Q – P
Is P ∪ Q a proper superset of P ∩ Q ?
Solution:

Question 5.
If A = (letters of word INTEGRITY) and B = (letters of word RECKONING), find
(i) A ∪ B
(ii) A ∩ B
(iii) A – B
(iv) B – A
Also verify that:
(a) n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
(b) n(A – B) = n(A ∪ B) – n(B)
= n(A) – n(A ∪ B)
(c) n(B – A) = n(A ∪ B) – n(A)
= n(B) – n(A ∩ B)
(d) n(A ∪ B) = n(A – B) + n(B – A) + n(A ∩ B).
Solution:

Question 6.
If ξ = {natural numbers between 10 and 40}
A = {multiples of 5} and
B = {multiples of 6}, then
(i) find A ∪ B and A ∩ B
(ii) verify that
n(A ∪ B) = B (A) + n(B) – n(A ∩ B).
Solution:

Question 7.
If ξ ={1,2, 3, …. 9}, A = {1, 2, 3, 4, 6, 7, 8} and B = {4, 6, 8}, then find.
(i) A’
(ii) B’
(iii) A ∪ B
(iv) A ∩ B
(v) A – B
(vi) B – A
(vii) (A ∩ B)’
(viii) A’ ∪ B’
Also verify that:
(a) (A ∩ B)’ = A’ ∪ B’
(b) n(A) + n(A’) = n(ξ)
(c) n(A ∩ B) + n((A ∩ B)’) = n(ξ)
(d) n(A – B) + n(B – A) + n(A ∩ B)
= n(A ∪ B).
Solution:

Question 8.
If 4 = {x : x ϵ W, x ≤ 10}, A. = {x : x ≥ 5} and B = {x : 3 ≤ x < 8}, then verify that:
(i) (A ∪ B)’ = A’ ∩ B’
(ii) (A ∩ B)’= A’ ∪ B’
(iii) A – B = A ∩ B’
(iv) B – A = B ∩ A’
Solution:

Question 9.
If n(A) = 20, n(B) = 16 and n(A ∪ B) = 30, find n(A ∩ B).
Solution:

Question 10.
If n ξ = 20 and n(A’) = 7, then find n(A).
Solution:

Question 11.
If n(ξ) = 40, n(A) = 20, n(B’) = 16 and n(A ∪ B) = 32, then find n(B) and n(A ∩ B).
Solution:

Question 12.
If n(ξ) = 32, n(A) = 20, n(B) = 16 and n((A ∪ B)’) = 4, find :
(i) n(A ∪ B)
(ii) n(A ∩ B)
(iii) n(A – B)
Solution:

Question 13.
If n(ξ) = 40, n(A’) = 15, n(B) = 12 and n((A ∩ B)’) = 32, find :
(i) n(A)
(ii) n(B’)
(iii) n(A ∩ B)
(iv) n(A ∪ B)
(v) n(A – B)
(vi) n(B – A)
Solution:

Question 14.
If n(A – B) = 12, n(B – A) = 16 and n(A ∩ B) = 5, find:
(i) n(A)
(ii) n(B)
(iii) n(A ∪ B)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 5 Playing with Numbers Check Your Progress

Question 1.
In a 2-digit number, sum of digits is 7. If the difference of 2 digit number and number obtained by reversing the digits is 9, then find the number.
Solution:

Question 2.
In a 3 digit number, the difference of hundred’s digit and unit’s digit is 5. Find the quotient when difference of 3-digit number and number obtained by reversing the digits is divided by 9.
Solution:

Question 3.
Without actual calculation, write the quotient when sum of 3 digit numbers 567, 675 and 756 is divided by
(i) 111
(ii) 18
(iii) 37
(iv) 3
Solution:

Question 4.
Find the values of the letters in each of the following and give reasons for the steps involved:

Solution:

Question 5.
If 923×783 is divisible by 11, what is the value of digit x?
Solution:

Question 6.
Check the divisibility of following numbers by 2, 3, 9 and 11:
(i) 76543
(ii) 65432
(iii) 98765436
(iv) 234567
Solution:

Question 7.
Check the divisibility of the following numbers by 5 or 10:
(i) 23565
(ii) 45270
Solution:

Question 8.
Check the divisibility of the following numbers by 4 or 8:
(i) 47596
(ii) 593024
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths