SETS - Testlabz.com |Online Practice Test and Study for ... which of the following collections are sets: (i) Collection of all the persons on earth (ii) Collection of all the difficult

1Class - VI Mathematics Question Bank

1. State which of the following collections are sets:

(i) Collection of all the persons on earth

(ii) Collection of all the difficult problems in your book on mathematics.

(iii) Collection of all the teachers in your school

(iv) Collection of most dangerous animals of India

(v) Collection of fat boys of your locality

(vi) Collection of all those students of your class whose age exceeds 15 years

(vii) Collection of all closed figures bounded by four line-segments

(viii) Collection of all musical instruments

(ix) Collection of all left-handed batsmen

(x) Collection of five most talented writers of India

Ans. (i) Yes (ii) No (iii) Yes (iv) No (v) No

(vi) Yes (vii) Yes (viii) Yes (ix) Yes (x) No

2. Describe the following sets in Roster form:

(i) Set of all natural numbers between 5 and 12

(ii) Set of all colours in a rainbow

(iii) Set of the months of the year, having 31 days

(iv) Set of all odd numbers between 60 and 75

(v) Set of all factors of 18

(vi) Set of all prime factors of 120

(vii) Set of all vowels in the word ‘MACHINE’

(viii) Set of all consonants in the word, ‘ALGEBRA’

(ix) Set of all 2-digit numbers, each having 8 as the sum of its digits.

(x) Set of all multiples of 7 which are less than 60.

Ans. (i) P = {6, 7, 8, 9, 10, 11}

(ii) P = {Violet, Indigo, Blue,Green, Yellow, Orange, Red}

(iii) P = {January , March , May, July, August, October, December}

(vi) P = {61, 63, 65, 67, 69, 71, 73} (v) P = {1, 2, 3, 6, 9, 18}

(vi) P = {2, 3, 5} (vii) P = {A, I, E}

1SETS


(viii) P = {L, G, B, R}

(ix) P = {17, 26, 35, 44, 53, 62, 71, 80}

(x) P = {7, 14, 21, 28, 35, 42, 49, 56}

3. Rewrite each of the following sets in Roster form:

(i) {x : x is a whole number, x < 15}

(ii) {x : x is an even number less than 16}

(iii) {x : x is a number which is neither prime nor composite}

(iv) {x : x is a perfect square, x < 50}

(v) {x : x is a natural number and a multiple of 5, x2 < 400}

(vi) {x : x is an even prime number}

(vii) All prime numbers between one and twenty.

(viii) Four cities of India whose names start with the letter J.

(ix) Single digit numbers which are perfect squares also.

(x) B = {x | x = 2n, n ∈ W and n < 5}

(xi) E = {x : x ∈ I and x2 < 10}

(xii) The set of whole numbers which are greater than 14 and divisible by 7.

Ans. (i) P = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}

(ii) P = {2, 4, 6, 8, 10, 12, 14} (iii) P = {1}

(iv) P = {1, 4, 9, 16, 25, 36, 49} (v) P = {5, 10, 15}

(vi) {2} (vii) {2, 3, 5, 7, 11, 13, 17, 19}

(viii) {Jaipur, Jothpur, Jalandhar, Jaunpur}

(ix) {0, 1, 4, 9} (x) {0, 2, 4, 6, 8}

(xi) {– 3, –2, –1, 0, 1, 2, 3}

(xii) {21, 28, 35, 42, ...}

4. State whether each of the following statements is true or false :

(i) 0 ∈ {x : x is a whole number} (ii) – 5 ∈ {x : x is a natural number}

(iii) 81 ∈ {x : x is prime number}

(vi) Two equivalent sets are always equal.

(v) Two equal sets are always equivalent.

(vi) {x : x is a letter in the word ‘APPLE’}= {x : x is letter in the word’ PALE’}

(vii) If A is the set of odd natural numbers and B is the set of even natural numbers,

then A B↔

(viii) {x : x is a natural number, 4 < x < 5} = { }.

(ix) {x : x is an integer, x is neither positive nor negative}= φ

(x) {x : x is a counting number, x is neither prime nor composite} is a singleton

set.


(xi) n (φ) = 0

(xii) φ and {0} are equivalent set.

Ans. (i) True (ii) False (iii) False (iv) False (v) True

(vi) True (vii) True (viii) True (ix) False (x) True

(xi) True (xii) False

5. Represent each of the following sets in Roster form and write the cardinal number

of each set :

(i) C = {x : x is an even natural number, x < 12}

(ii) D = Set of all continents in the world

(iii) F = Set of months having less than 30 days.

(iv) H = {x : x is an odd prime number, x < 19}.

(v) M = { x : x is a natural number, 3 < x < 4}

(vi) N = {x : x is a composite number, 10 < x < 18}

Ans. (i) C = {2, 4, 6, 8, 10}, n (C) = 5

(ii) D = {Asia, North America, South America, Africa, Europe, Australia,

Antartica}, n(D) = 7

(iii) F = {February}, n (F) = 1 (iv) H = {3, 5, 7, 11, 13, 17}, n (H) = 6

(v) M = { }, n(M) = 0 (vi) N = {12, 14, 15, 16}, n(N) = 4.

6. Let A = {2, 4, 6, 8, 10} and B = {x : x is a whole number, x < 5}. Find n(A) and

n(B). Are A and B equivalent sets ?

Ans. A = {2, 4, 6, 8, 10}, B = { 0, 1, 2, 3, 4}, n(A) = 5, n(B) = 5. Yes A and B are

equivalent sets.

7. Which of the following are equal sets ?

(i) A = {x | x is a counting number, 1 < x < 3} and B = {x | x is prime, x is even}.

(ii) C = {x | x is prime factor of 24} and D = {x | x is prime, x < 4}

(iii) G = {x | x is a whole number, x < 8} and H = {x | x is a counting number, x < 9}

Ans. (i) A = B (ii) C = D (iii) G ≠ H.

8. Write each of the following sets in Roster form and also in set builder form :

(i) the set of all even numbers that lie between 15 and 32.

Ans. {16, 18, 20 .....30} ; {x : x is an even number and 15 < x < 32}

(ii) {last four months of a year}

Ans. {September, October, November, December}; {x : x is the last four months of a

year}

(iii) {Single digit number which are perfect square}

Ans. {0, 1, 4, 9}; {x : x is a and one digit perfect square number}

(iv) the set of consonants in the word ‘PERMUTATION’

Ans. {P,R, M, T, N}; {x : x is a consonant in the word ‘PERMUTATION’ and A ∩ B}


9. Find A ∪ Β, when :

(i) A = {1, 2, 4, 8, 16} and B = {2, 3, 4, 6, 12, 24}

(ii) A = Set of all vowels in English alphabet and B = Set of first five letters of

English alphabet

(iii) A = Set of all the letters of the word ‘POPULATION’ and B = Set of all the

letters of the word ‘PEOPLE’

(iv) A = Set of all non-negative integers and B = Set of all non-positive integers

Ans. (i) A B∪ = {1, 2, 3, 4, 6, 8, 12, 16, 24} and A B∩ = {2, 4}

(ii) Α = {a, e, i, o, u} and B = {a, b, c, d, e} A B∪ = {a, b, c, d, e, i, o, u},

A B∩ = {a, e}

(iii) A = {P, O, U, L, A, T, I, N} and B = {P, E, O, L}

A B∪ = {P, O, U, L, A, T, I, N, E} and A B∩ = {P, O, L}

(iv) A = {0, 1, 2, 3, ....} and B = {0, – 1, – 2, – 3....}

A B∪ = Set of all integers, A B∩ = {0}

10. Let A = {1, 2, 3, 4} and B = {2, 3, 5, 7 } Verify that

( ) ( ) ( ) ( )n A B n A n B n A B∪ = + − ∩ .

Ans. A = {1, 2, 3, 4}, n(A) = 4 and B = {2, 3, 5, 7}, n(B) = 4 A B∪ = {1, 2, 3, 4, 5, 7},

n( A B∪ ) = 6, A B∩ = { 2, 3 }, n( A B∩ ) = 2

n( A B∪ ) = n(A) + n(B) – n( A B∩ ) ⇒ 6 = 4 + 4 – 2 = 6, it is verified.

11. Let A = { x : x ∈N, x is a multiple of 4, x < 20} and B = { x : x ∈ N, x is a multiple

of 8, x < 20 }. Find A B∪ and A B∩ . What do you conclude ?

Ans. A = {4, 8, 12, 16} and B = {8, 16}

A B∪ ={x : x ∈ Ν, x is a multiple of 4, x < 20} A B∩ = {x : x ∈ N, x is a

multiple of 8, x < 20} A B∪ = A and A B∩ = B

12. Let C = {x : x ∈ N, x is even} and D = {x : x ∈ N, x is prime}

State whether the sets C and D are disjoint or intersecting.

Ans. C D∩ = {2} ≠ φ. Thus C and D are intersecting sets.

13. Let A = {5, 7, 9, 11} and B = {6, 8, 10, 12}. Verify that : ( )n A B∪ = n(A) + n(B).

Ans. A = {5, 7, 9, 11}, n(A) = 4 and B = {6, 8, 10, 12}, n(B) = 4

A B∪ = {5, 6, 7, 8, 9, 10, 11, 12}, ( )n A B∪ = 8

( )n A B∪ = n(A) + n(B) 8 ⇒ 8 = 4 + 4 ⇒ 8 = 8, its verified.

14. Write two sets A and B such that n(A)= 3, n(B) = 4, n(A ∪ B) = 7.

Ans. A = {1, 2, 3} B = {4, 5, 6, 7}

∴ n(A) = 3, n(B) = 4 and ( )A B∪ = {1, 2, 3, 4, 5, 6, 7}, n( A B∪ ) = 7


15. State, if the given pairs of sets are equal sets or equivalent sets:

(i) {Natural numbers less than five} and {Letters of the word ‘BOAT’}.

(ii) {2, 4, 6, 8, 10} and {even natural number less than 12}

(iii) {a, b, c,d} and { , 8,∆ , ∇ }.

(iv) {Days of the week} and {Letters of the word ‘HONESTY’}

(v) {Letters of the word ‘MEMBER’} and {Letters of the word ‘REMEMBER’}

Ans. (i) Equivalent (ii) Equal (iii) Equivalent

(iv) Equivalent (vi) Equal

16. State giving reasons, which of the following pairs of sets are disjoint sets or over-

lapping sets:

(i) A = {Girls with ages below 15 years} and B = {Girls with ages above 15

years}

(ii) A = {Natural numbers between 35 and 60} and B = {Natural numbers be-

tween 50 and 80}

(iii) P = {Students of class IX studying in I.C.S.E. Board} and Q = {Students of

class IX}

(iv) A = {Natural numbers multiples of 3 and less than 30} and B = {Natural

numbers divisible by 4 and between 20 and 45}

(v) P = {Letters in the word ‘ALLAHABAD’} and Q = {Letters in the word

‘MUSSOORIE’}

Ans. (i) Disjoint set; because no girl can be of age below 15 years and also above 15

years

(ii) Overlapping sets; because numbers from 50 to 59 are common to both the

sets.

(iii) Overlapping sets; because students of class IX studying in I.C. S.E. board

are common.

(iv) Overlapping sets; because natural number 24 is common to both the sets.

(v) Disjoint sets; because no letter is common to both the sets.

17. If set A = {2, 3, 4, 5, 6}. State, whether the following statements are true or false :

(i) 2 ∈ A (ii) 5, 6 ∈ A (iii) 3, 4, 7 ∈ A (iv) 2, 8 ∈ A

Ans. (i) True (ii) True (iii) False (iv) False

18. Two sets P and Q are given as follows : P = {3, 5, 7, 9,11, 13} and Q = {8, 10, 12,

14, 16, 18}. State, giving reasons, which of the following are true :

(i) 13 ∈ P, 9 ∈ P but 13 + 9 ∉ P

(ii) 3 ∈ P, 13 ∈ Q but 13 – 3 ∉ Q

(iii) 7 ∉ Q, 9 ∈ Q but 7 + 9 ∉ Q


Ans. (i) True. 13 + 9 = 22, which is not in set P.

(ii) False. 3 ∈ P.but 13 ∉ Q.

(iii) True. 7 + 9 = 16, which belongs to set Q.

19. Write down the elements of :

(i) Set A, if set A contains the squares of the first five whole numbers.

(ii) Set B, if set B contains the cubes of first three even natural numbers.

(iii) Set C, if 20 and 40 ; all divisible by 4.

(iv) Set E, if set E contains natural numbers between 15 and 40; each divisible by 3

and 4.

Ans. (i) {0, 1, 4, 9, 16} (ii) {8, 64, 216} (iii) {24, 28, 32, 36} (iv) {24, 36}

20. Write which of the following statements are true. In case a statement is incorrect,

mention why.

(i) {e} ∈ {a, e, i, o,u}

Ans. {e} ∈ {a, e, i, o, u} false because {e} is a different set and not an element.

(ii) b ∈ {a, e, i, o, u}

Ans. b ∈{a, e, i, o, u} false because b is not a vowel. It is not in the set.

(iii) b ∉ {a, e, i, o, u}

Ans. b ∉ {a, e, i, o, u} true because b is not an element of the set of vowels.

(iv) a, e, u ∈ {a, e, i, o, u}

Ans. a, e, u, ∈ {a, e, i, o,u} true because all elements , a, e, u are belong in the set

21. If A = {2, 3, 4, 5}, B = {1, 3, 5, 7} and C = {4, 5, 6, 7}; find :

(i) A B∪ (ii) A ∪ C (iii) ( ) ( )A B A C∪ ∩ ∪

(iv) ( )A B C∪ ∩ Is ( ) ( ) ( )A B A C A B C∪ ∩ ∪ = ∪ ∩ ?

Ans. (i) A B∪ = {1, 2, 3, 4, 5, 7} (ii) A C∪ = {2, 3, 4, 5, 6, 7}

(iii) A B∪ = {1, 2, 3, 4, 5, 7} A C∪ = {2, 3, 4, 5, 6, 7}

∴ ( )A B∪ ( )A C∩ ∪ = {2, 3, 4, 5, 7}

(iv) B C∩ = {5, 7}, ∴ ( )A B C∪ ∩ = A {2, 3, 4, 5, 7}

From (iii) ( ) ( )A B A C∪ ∩ ∪ = {2, 3, 4, 5, 7}

⇒ ( )A B C∪ ∩ = ( ) ( )A B A C∪ ∩ ∪

22. If A = {a, b, c, d} B = {c, d, e, f} and C = {b, d, f, g} ; find:

(i) A B∩ (ii) A C∩ (iii) ( ) ( )A B A C∩ ∩ ∩

(iv) ( )A B C∩ ∪ Is ( ) ( ) ( )A B A C A B C∩ ∪ ∩ = ∩ ∪ ?

Ans. (i) A B∩ = {c, d} (ii) A C∩ = {b, d}

(iii) A B∩ = {c, d} A C∩ = {b, d}

∴ ( ) ( )A B A C∩ ∪ ∩ = {b, c, d}

(iv) B C∪ = {b, c, d, e,f, g}


∴ ( )A B C∩ ∪ = {b, c, d}

From (iii) ( ) ( )A B A C∩ ∪ ∩ = {b, c, d} ⇒ ( ) ( ) ( )A B C A B A C∩ ∪ = ∩ ∪ ∩

23. Let A = Set of natural numbers less than 8, B = {even natural numbers less than 12},

C = {multiples of 3 between 5 and 15} and D = {multiples of 4 greater than 6 and

less than 20} ; find

(i) B C∪ (ii) A D∪ (iii) C D∪ (iv) A C∩

(v) ( )B C A∩ ∪ (vi) ( )D A B∪ ∩ (vii) ( ) ( )A C B D∩ ∪ ∩

(viii) ( ) ( ).B D C A∩ ∩ ∪

Ans. Given, A = {1, 2, 3, 4, 5, 6, 7}, B = {2, 4, 6, 8, 10}, C = {6, 9, 12}, D = {8, 12, 16}

(i) B C∪ = {2, 4, 6, 8, 9, 10, 12}

(ii) A D∪ = {1, 2, 3, 4, 5, 6, 7, 8, 12, 16}

(iii) C D∪ = {6, 8, 9, 12, 16} (iv) A C∩ = {6}

(v) B C∩ = {6} ∴ ( )B C A∩ ∪ = {1, 2, 3, 4, 5, 6, 7}

(vi) D A∪ = {1, 2, 3, 4, 5, 6, 7, 8, 12, 16} ∴ ( )D A B∪ ∩ = {2, 4, 6, 8}

(vii) A C∩ = {6} B D∩ = {8} ∴ ( ) ( )A C B D∩ ∪ ∩ = {6, 8}

(viii) B D∪ = {2, 4, 6, 8, 10, 12, 16} C A∪ = {1, 2, 3, 4, 5, 6, 7, 9, 12}

∴ ( ) ( )B D C A∪ ∩ ∩ = {2, 4, 6, 12}

24. If set A = {3, 4, 5, 6} and set B = {2, 4, 6, 8} ; find :

(i) A – B (ii) B – A

Ans. A = {3, 4, 5, 6} and B = {2, 4, 6, 8}

(i) A – B = {Those elements of A which are not in set B} = {3, 5}

(ii) B – A = {Those elements of B which are not in set A} = {2, 8}

25. Given set A = {2, 4, 6, 8, 10, 12}, set B = {3, 6, 9, 12, 15, 18}; and set

C = {0, 6, 12, 18}; find :

(i) A – B (ii) B – C (iii) C – A (iv) A – C

Ans. Given A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12, 15, 18} C = {0, 6, 12, 18}

(i) A – B = {Those elements of A which are not in B} = {2, 4, 8, 10}

(ii) B – C = {Those elements of B which are not in set C} = {3, 9, 15}

(iii) C – A = {Those elements of C which are not in set A} = {0, 18}

(iv) A – C = {Those elements of A which are not in set C} = {2, 4, 8, 10}

26. Given : P = {a, c, d, m} Q = {c, e, m, x} and R = {a, e, i, o}. Find :

(i) P – R (ii) Q – P (iii) R – Q

Ans. P = { a, c, d, m}, Q = {c, e, m, x}, and R = {a, e, i, o}

(i) P – R = {c, d, m} (ii) Q – P = {e, x} (iii) R – Q = {a, i, o}


27. If A = {counting numbers between 30 and 40}, B = {counting numbers between 20

and 50 which are divisible by 4}. Find : (i) A – B (ii) B – A

Ans. Given A = {counting numbers between 30 and 40} = {31, 32, 33, 34, 35, 36, 37,

38, 39}. B = {counting numbers between 20 and 50 which are divisible by 4} =

{24, 28, 32, 36, 40, 44, 48}

(i) A – B = {those elements of A which are not in set B} = {31, 33, 34, 35, 37,

38, 39}

(ii) B – A = {those elements of B which are not in set A} = {24, 28, 40, 44, 48}

28. If P = {letters in the word ‘BANARAS’}, Q = {letters in the word‘BHARAT’}

and R = {letters in the word ‘BHATINDA} Find:

(i) P – Q (ii) R – Q (iii) P – R.

Ans. P = {B, A, N, A, R, A, S}, Q = {B, H, A, R, A, T}, R = {B, H, A, T, I, N, D, A}

(i) P – Q = {N, S} (ii) R – Q = {I, N, D} (iii) P – R = {R, S}

29. If A = {5, 7, 8, 9}, B = {3, 4, 5, 6} and C = {2, 4, 6, 8, 10}; find :

(i) n(A) + n(B) (ii) ( )n A B∪ (iii) ( )n A B∩

(iv) ( ) ( )n A B n A B∪ + ∩ (v) ( )n B C∪ (vi) ( ) ( ) – ( )n B n C n B C+ ∩

Is n(A) + n(B) = ( ) ( )n A B n A B∪ + ∩ ? Is ( ) ( ) ( ) – ( )?n B C n B n C n B C∪ = + ∩

Ans. (i) n (A) = 4 n(B) = 4 ∴ n(A) + n(B) = 4 + 4 = 8

(ii) A B∪ = {3, 4, 5, 6, 7, 8, 9} ∴ ( )n A B∪ = 7

(iii) A B∩ = {5} ∴ ( )n A B∩ = 1

(iv) ( ) ( )n A B n A B∪ + ∩ = 7 + 1 [from part (ii) and (iii) ] = 8

(v) B C∪ = {2, 3, 4, 5, 6, 8, 10} ∴ ( )n B C∪ = 7

B C∩ = {4, 6} and ( )n B C∩ = 2

∴ n(B) + n(C) – ( )n B C∩ = 4 + 5 – 2 = 7

Now, from part (i) and (iv)

Yes, n (A) + n(B) = ( ) ( )n A B n A B∪ + ∩ and from part (v) and (vi)

Yes, ( )n B C∪ = n (B) + n(C) – ( )n B C∩

30. If P = {4, 8, 12, 16, 20}, Q = {2, 4, 6, 8, 10, 12, 14, 18, 20} and R = {a, b, c, d, e}

State true or false :

(i) n (P) = n (R) (ii) n (P) = n (Q) (iii) n (Q) – n (R) = n (P)

(iv) n (Q) = 2 n (R)

Ans. n (P) = 5, n (Q) = 9 and n (R) = 5

(i) n(P) = n (R) = 5 True.

(ii) n (P) ≠ n (Q) ⇒ 5 ≠ 9 which is false.


(iii) n (Q) – n (R) = n (P)

⇒ 9 – 5 = 5 ⇒ 4 = 5 which is false.

(iv) n (Q) = 2.n (R)

⇒ 9 = 2 (5) ⇒ 9 = 10 which is false.

31. If O = {odd numbers less than 12} and E = {even numbers between 7 and 17}, show

that : n(O) – n(E) = 1.

Ans. Here, O = {1, 3, 5, 7, 9, 11} and E = {8, 10, 12, 14, 16}

⇒ n (O) = 6 and n (E) = 5

Subtracting n (O) – n (E) = 6 – 5 = 1 Hence proved.

32. Let P = {x : x is a letter in the word CHANDIGARH}Q = {x : x is a letter in the word

JAMNAGAR}

(i) Find P ∪ Q and P ∩ Q

Ans. P ∪ Q = {CH, A, N, D, I, G, J, M} P Q∩ = {A, N, G, R}

(ii) Find n(P), n(Q), ( )n P Q∪ and ( )n P Q∩

Ans. n(P) = 8, n (Q) = 6 ; ( )n P Q∪ = 10 ; ( )n P Q∩ = 4

(iii) Verify that ( )n P Q∪ = n(P) + n(Q) – ( )n P Q∩

Ans. LHS = ( )n P Q∪ = 10 RHS = n(P) + n(Q) – ( )n P Q∩ = 8 + 6 – 4 = 10

LHS = RHS

(iv) State whether the sets P and Q are join or disjoint.

Ans. ( )n P Q∪ = 10, ( )n P Q∩ = 4 ∴ P and Q are joint sets.

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

B = {x | x ∈ N, x < 40 and x is a multiple of 7} and C = {x |x ∈ N, x < 40 and x is a

multiple of 8} State whether the following pairs of sets are disjoint or overlapping

:

(i) A and B (ii) A and C (iii) B and C

Ans. A = {6, 12, 18, 24, 30, 36}, B = {7, 14, 21, 28, 35}, C = {8, 16, 24, 32}

(i) A B φ∩ = thus, A and B are disjoint (ii) A C∩ = {24} thus A and C are over-

lapping

(iii) ,B C φ∩ = B and C are disjoint

34. Represent each of the following pairs of sets by Venn diagram:

(i) A = {2, 3, 5, 7, 9} and B = {4, 8, 12, 16, 18}

(ii) C = {a, e, i, o, u} and D = {c, d, e, f, h, i}

(iii) E = { 5, 7, 11, 13} and F = {5, 7, 9, 11, 13, 15, 17}

(iv) M = {All prime factors of 42} and N = {All prime factors of 165}


(v) P = {Multiples of 3 less than 20}and Q = {Multiples of 2 less than 20}

(vi) R = {All boys of your class}, S = {All girls of your class}

(vii) X = {People living in India}, Y = {People living in Punjab}

Ans. (i) A = { 2, 3, 5, 7, 9} and B = {4, 8, 12, 16, 18} 2

5 7

3

9A

4

8 1812

16

B

(ii) C = {a, e, i, o, u} and D = {c, d, e, f, g, h, i}a

ou

i

ec d

f

hg

C D

(iii) E = {5, 7, 11, 13} and F = {5, 7, 9, 11, 13, 15, 17} 57

11

13

915

17

EF

(iv) M = {All prime factors of 42} = {2, 3, 7}

N = { All prime factors of 165} = {3, 5, 11}

(v) P = {Multiples of 3 less than 20}

= {3, 6, 12, 15, 18}

Q = {Multiples of 2 less than 20}

= {2, 4, 6, 8, 10, 12, 14, 16, 18}

(vi) R = {All boys of your class},

S = {All girls of your class}

(vii) X = {People living in India}, Y = {People living in Punjab}

P eop le liv in g inIndia ou ts id e

P unjab

Pe opleliv ing inPu nja b

Y

X

34. From the given Venn diagram, find the following:

(i) L (ii) M (iii) L M∩ (iv) L M∪

9

315

61218

2 48

1014

16P Q

Boys of your class

R

Girls of your class

S


Ans. (i) L = {s, p, e, a, k, r}

(ii) M = {f, l, i, g, h, t}

(iii) L M∩ = {s, p, e, a, k, r} ∩{f, l, i, g, h, t} = φ

(iv) L M∪ = {s, p, e, a, k, r} ∪{f, l, i, g, h, t} = {s, p, e, a, k,r, f, l, i, g, h, t}

35. Use the given Venn-diagram to find the following sets :

(i) P (ii) Q (iii) P Q∪ (iv) P Q∩

Ans. (i) P = {a, b, c, d} (ii) Q φ=

(iii) P Q∪ = {a, b, c, d} (iv) P Q φ∩ =

36. From the disjoint sets, shown alongside, find the sets :

(i) X (ii) Y (iii) X Y∪ (iv) X Y∩

Ans. (i) X = {0, 4, 5, 6, 8, 10, 13} (ii) Y = {o, x, y, z, m, n}

(iii) X Y∪ = {0, 4, 5, 6, 8, 10, 13, o, x, y, z, m, n} (iv) X Y∩ = { } = φ

37. Given : A = Set of flowers, B = Set of red flowers and C = Set of flowers which

bloom in winter. Write each of the following sets in words and represent them by

Venn-diagram by shading the portion:

(i) A B∩ (ii) B C∩ (iii) .A C∩

Ans. (i) Set of red flowers ;

(ii) Set of red flowers which bloom in winter,

(iii) Set of flowers which bloom in winter.

38. Let A = {Natural numbers between 10 and 40; each divisible by 3}, B = {Natural

numbers upto 40; each divisible by 4}.

(i) Write each set in roster form.

(ii) Draw a Venn-diagram to represent the relationship between A and B.

Ans. (i) A = {12, 15, 18, 21, 24, 27, 30, 33, 36, 39}

(ii) B = {4, 8, 12, 16, 20, 24, 28, 32, 40}

sek

par

L

fih

lgt

M

ab

c

d

P Q

4

6 0

8 10

135

X Ym

o xz

y

n

A

B

B C

A

C

15 18

2127

1224

3633

3039

4

16

28

8

20

3218

M N


39. For each of the following Venn-diagrams write the set A B∪ :

(i) 0

1

3

58

2

9

A B

(ii)

B

A

A

6

3

82

(iii)

A

36

87

B

2

3 7

Ans. (i) {0, 1, 2, 3, 5, 8, 9} (ii) {2, 3, 6, 8}

(iii) {2, 3, 6, 7, 8}

40. If P = {all months of a year} and Q = {months of a year whose name begin with letter

M}, find P Q∪ and .P Q∩ State whether the sets P and Q are joint or disjoint.

Ans. P = {Jan, Feb, March, April, May, June, July, Aug, Sept., Oct., Nov., Dec.}

Q = {March, May} P Q∪ = {all months of year}, P Q∩ = {March, May}

The sets are joint because March and May are common elements.

41. Let A = {x | x ∈ N, x is a multiple of 6 less than 50} and B = {x |x ∈ W, x is a multiple

of 8 less than 50} Show the relationship between these sets by a Venn diagram.

Ans. A = {6, 12, 18, 24, 30, 36, 42, 48},

B = {0, 8, 16, 24, 32, 40, 48}

So, these sets are joint.

42. From the given Venn diagram, find the following:

(i) E (ii) F (iii) E F∩ (iv) E F∪ Ans. (i) E = {1, 3, 7, 21} (ii) F = {1, 2, 3, 6, 7, 14, 21, 42}

(iii) E F∩ = {1, 3, 7, 21} ∩ {1, 2, 3, 6, 7, 14, 21, 42}

= {1, 3, 7, 21} = E

(iv) E F∪ = {1, 3, 7, 21} ∪ {1, 2, 3, 6, 7, 1421, 42}

= {1, 2, 3, 6, 7, 14, 21, 42} = F

43. From the adjacent Venn diagram, write the following sets in Roster form:

(i) P (ii) Q (iii) P Q∩ (iv) P Q∪

Ans. In this Venn diagram :

P = {a, b, c, d, e, p, q, r}, Q = {a, b, e, f, g, h, i, k}

(iii) P Q∩ = {a, c, e}

(iv) P Q∪ = {a, b, c, d, e, p, q, r, f, h, i, k}

44. Observe the following Venn diagram and then represent the following in Roster

form. (i) Set M (ii) Set N

(iii) M N∪ (iv) M N∩

Ans. (i) M = {1, 3, 5, 7, } (ii) N = {2, 4, 6, 8}

(iii) M N∪ = {1, 2, 3, 4, 5, 6, 7, 8} (iv) M N∩ = φ

6

30

42

12

36

18

24

48

0

32

8

1640

E

F

1

7

3

21

26 14

42

1

7

3

5

2

4 6

8

M N

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SETS - Testlabz.com |Online Practice Test and Study for ... which of the following collections are sets: (i) Collection of all the persons on earth (ii) Collection of all the difficult