1 Marks Questions

Which of the following are sets? Justify your answer.

1. The collection of all the months of a year beginning with letter M

Ans. Set

2. The collection of difficult topics in Mathematics. Let A = {1,3,5,7,9}. Insert the appropriate symbol or in blank spaces :– (Question- 3,4)

Ans. Not a set

3. 2—A

Ans. ∈

4. 5 – A

Ans. ∈

5. Write the set A = { x : x is an integer, –1 x < 4} in roster form

Ans. A = {–1, 0, 1, 2, 3}

6. List all the elements of the set,

× : × ϵ Z, - 1/2 < × < 11/2}

Ans. A = { 0,1,2,3,4,5}

7. Write the set B = {3,9,27,81} in set-builder form. Which of the following are empty sets? Justify.

Ans. B = { x : x = , n ϵ N and 1 ≤ n ≤ 4}

8. A = { x : x ϵ N and 3 <x <4}

Ans. Empty set

9. B = { x : x ϵ N and = x}Which of the following sets are finite or Infinite? Justify.

Ans. Non-empty set

10. The set of all the points on the circumference of a circle.

Ans. Infinite set

11. B = { x : x ϵ N and x is an even prime number}

Ans. Finite set

12. Are sets A = { –2,2}, B = { x : x ϵ Z, –4 = 0} equal? Why?

Ans. Yes

13. Write (–5,9] in set-builder form

Ans. { x : x ϵ R, –5 < x ≤ 9}

14. Write { x : –3 ≤ x <7} as interval.

Ans. [ –3,7)

15. If A = { 1,3,5}, how many elements has P(A)?

Ans. 2³ = 8

16. Write all the possible subsets of A = {5,6}. If A = {2,3,4,5}, B = { 3,5,6,7}

Ans. ∅, { 5}, {6}, {5,6}

17. A ∪ B

Ans. A ∪ B = {2,3,4,5,6,7}

18. A ∩ B

Ans. A ∩ B = {3, 5}

19. If A = {1,2,3,6} , B = {1, 2, 4, 8} find B – A

Ans. B – A = {4,8}

20. If A = {p, q}, B = {p, q, r}, is B a superset of A? Why?

Ans. Yes, because A is a subset of B

21. Are sets A = {1,2,3,4}, B = { x : x ϵ N and 5 ≤ x ≤ 7} disjoint? Why?

Ans. es, because A ∩ B = ∅

22. If X and Y are two sets such that n(X) = 19, n(Y) = 37 and n(X ∩ Y) = 12, find n(X ∪ Y).

Ans. n(X ∪ Y) = 44

23.Describe the set in Roster form

Ans. { 17, 26, 35, 44, 53, 62, 71, 80 }

24.Are the following pair of sets equal? Give reasons.

A = { x:x is a letter in the word FOLLOW}

B = { y:y is a letter in the word WOLF}

Ans. A= {F, O, L, W}

B = {W, O, L, F }

Hence A=B

25.Write down all the subsets of the set {1,2,3}

Ans.

26.Let A = { 1,2,{3,4,},5} is

Ans. {3,4} is an elements of sets A, therefore is a set containing element {3,4} which is belongs to A

Hence A is correct

27.Draw venn diagram for

Ans. = U- (A∩B)

28.Write the set in roster form A = The set of all letters in the word T R I G N O M E T R Y

Ans. A = {T, R, I, G, N, O, M, E, Y}

29.Are the following pair of sets equal? Give reasons

A, the set of letters in “ALLOY” and B, the set of letters in “LOYAL”.

Ans. A = {A, L, O, Y}

B = {L, O, Y, A}

Hence A = B

30.Write down the power set of A , A = {1, 2, 3}

Ans.

31.A = {1, 2, {3, 4}, 5} which is incorrect and why. (i) {3, 4} A (ii) {3, 4} A

Ans.{3, 4} is an element of set A.

Hence

32.Fill in the blanks.

(i) --------

(ii) = ---------

(iii) --------

Ans. (i)U

33.Write the set in the set builder form.

Ans.

34.Is set C = { x : x – 5 = 0} and E = {x : x is an integral positive root of the equation x² – 2x – 15 = 0} are equal?

Ans. C = {5}

35.Write down all possible proper subsets of the set {1, {2}}.

Ans.

36.State whether each of the following statement is true or false.

(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.

(ii) {2, 6, 10} and {3, 7, 11} are disjoint sets

Ans. (i)

Hence false

(ii)

true

37.Fill in the blanks

(i) (A B)´ = ---------

(ii) (A ∩ B)ʹ = ---------

Ans. (A ∪ B= ∩

(A ∩ B= ∪

38.Write the set of all vowels in the English alphabet which precede k in roster Form

Ans. A = {b, c, d, f, g, h, j}

39.Is pair of sets equal? Give reasons.

A = {2, 3} B = x : x is solution of x² + 5x + 6 = 0}

Ans. A = {2, 3}

B = {- 2, - 3}

A ≠ B

[∴ x² + 5x + 6 = 0

x² + 3x + 2x + 6 = 0

x = - 2 – 3

40.Write the following intervals in set builder form: (-3, 0) and [6, 12]

Ans. (- 3, 0) = {x : x ϵ R, - 3 < x < 0}

[6, 12] = {x : x ϵ R, 6 ≤ x ≤ 12}

41.If X = {a, b, c, d}

Y = {f, b, d, g}

Find X – Y and Y – X

Ans. X – Y = {a, b, c, d} – {f, b, d, g}

= {a, c}

Y – X = {f, b, d, g} – {a, b, c, d}

= {f, g}

42.If A and B are two given sets, Then represent the set (A – B, using Venn diagram.

Ans. (A – B= ∪ - (A – B)

43.List all the element of the set A = { x : x is an integer x² ≤ 4}

Ans. {-2, -1, 0, 1, 2}

44.From the sets given below pair the equivalent sets.

A = { 1, 2, 3}, B = {x, y, z, t}, C = {a, b, c} D = {0, a}

Ans. A = {1, 2, 3} B = {a, b, c} are equivalent sets

45.Write the following as interval

(i) {x : x ϵ R, - 4 < x ≤ 6}

(ii) {x : x ϵ R, 3 ≤ x ≤ 4}

Ans. (i) (-4, 6]

(ii) [3, 4]

46.If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} Find (A ∩ B) ∩ ( B ∪ C)

Ans. A ∩ B = {7, 9, 11}

B ∪ C = {7, 9, 11, 13, 15}

(A ∩ B) ∩ (B ∪ C) = {7, 9, 11}

47.Write the set in set builder form.

Ans.

6 Marks Questions

1. In a survey it is found that 21 people like product A, 26 people like product B and 29 like product C. If 14 people like product A and B, 15 people like product B and C, 12 people like product C and A, and 8 people like all the three products. Find

(i) How many people are surveyed in all?

(ii) How many like product C only?

Ans. Hint : Let A, B, C denote respectively the set of people who like product

A, B, C.

a, b, c, d, e, f, g – Number of elements in bounded region

(i) Total number of Surveyed people = a + b + c + d + e + f + g = 43

(ii) Number of people who like product C only = g = 10

2. A college awarded 38 medals in football, 15 in basket ball and 20 in cricket. If these medals went to a total of 50 men and only five men got medals in all the three sports, how many received medals in exactly two of the three sports?

Ans. people got medals in exactly two of the three sports.

Hint :

f = 5

a + b + f + e = 38

b + c + d + f = 15

e + d + f + g = 20

a + b + c + d + e + f + g = 50

we have to find b + d + e

3.There are 200 individuals with a skin disorder, 120 had been exposed to the chemical C₁, 50 to chemical C₂, and 30 to both the chemicals C₁ and C₂. Find the number of individuals exposed to

(1) chemical C₁ but not chemical C₂

(2) chemical C₂ but not chemical C₁

(4) chemical C₁ or chemical C₂

Ans. A denote the set of individuals exposed to the chemical C₁ and B denote the set of individuals exposed to the chemical C₂

n(U) = 200, n(A) = 120, n(B) = 50, n(AB) = 30

(i) n(A-B) = n(A) – n(AB)

=120-30=90

(ii)n(B-A) = n(B) – n(AB)

=50-30 = 20

(iii)n(A∪B) =n(A)+ n(B)-n(AB)

=120+50-30

=140

4.In a survey it was found that 21 peoples liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people like C and A, 15 people like B and C and 8 liked all the three products. Find now many liked product C only.

Ans. a + b + c + d = 21

b + c + e + f = 26

c + d + f + g = 29

b + c = 14,c + f =15,c + d = 12

c = 8

d = 4,c = 8,f = 7,b = 6,g = 10,e = 5,a = 3

like product c only = g = 10

5.A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medal in all the three sports, how many received medals in exactly two of the three sports?

Ans. Let A, B and C denotes the set of men who received medals in football, basketball and cricket respectively.

n (A) = 38, n (B) = 15, n (C) = 20

n (A B C) = 58 and n (A ∩ B ∩ C) = 3

n (A B C) = n (A) + n (B) + n(C) – n (A ∩ B) – n (B ∩ C) – n (C ∩ A) + n (A ∩ B ∩ C)

58 = 38 + 15 + 20 – (a + d ) – (d + c) – (b + d) + 3

18 = a + d + c + b + d

18 = a + b + c + 3d

18 = a + b + c + 3 3

9 = a + b + c

6.In a survey of 60 people, it was found that 25 people read news paper H, 26 read newspaper T,

26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three

newspaper. Find

(i) The no. of people who read at least one of the newspapers.

(ii) The no. of people who read exactly one news paper.

Ans. a + b + c + d = 25

b + c + e + f = 26

c + d + f +g = 26

c + d = 9

b + c = 11

c + f = 8

c = 3

f = 5, b = 8, d = 6, c = 3, g = 12

e = 10, a = 8

(i) a + b + c + d + e + f + g = 52

(ii) a + e + g = 30

7.These are 20 students in a chemistry class and 30 students in a physics class. Find the number of students which are either in physics class or chemistry class in the following cases.

(i) Two classes meet at the same hour

(ii) The two classes met at different hours and ten students are enrolled in both the courses.

Ans. Let C be the set of students in chemistry class and P be the set of students in physics class.

n (C) = 20, n (P) = 30

(i)

(ii)

8.In a survey of 25 students, it was found that 15 had taken mathematics, 12had taken physics and 11 had taken chemistry, 5 had taken mathematics and chemistry, 9 had taken mathematics and physics, 4 had taken physics and chemistry and 3 had taken all three subjects.

Find the no. of students that had taken

(i) only chemistry (ii) only mathematics (iii) only physics

(iv) physics and chemistry but mathematics (v) mathematics and physics but not chemistry (vi) only one of the subjects (vii) at least one of three subjects

(viii) None of three subjects.

Ans.

9. In a survey of 100 students, the no. of students studying the various languages were found to be English only 18, English but not Hindi 23, English and Sanskrit 8, English 26, Sanskrit 48, Sanskrit and Hindi 8, no language 24. Find

(i) How many students were studying Hindi?

(ii) How many students were studying English and Hindi?

Ans. ∪ = 100, a = 18

a + e = 23, e + g = 8

a + e + g + d = 26

e + g + f + c = 48

g + f = 8

so, e = 5, g = 3, d = 0, f = 5, c = 35

(i) d + g + f + b = 0 + 3 + 5 + 10 = 18

(ii) d + g = 0 + 3 = 3

10. In a class of 50 students, 30 students like Hindi, 25 like science and 16 like both.

Find the no. of students who like

(i) Either Hindi or science

(ii) Neither Hindi nor science.

Ans. Let ∪ = all the students of the class ,H = students who like Hindi

S = Students who like Science

(i) n ( H ∪ S) = n (H) + n (S) – n (H ∩ S)

= 30 + 25 – 16

= 39

(ii) n (∩) = n (H ∪ S

= ∪ - n (H ∪ S)

= 50 – 39

= 11

11.In a town of 10,000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C. 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three papers. Find the no. of families which buy

(i) A only (ii) B only (iii) none of A, B, and C.

Ans. x + a + c + d = 4000

y + a + d + b = 2000

z + b + c + d = 1000

a + d = 500, b + d = 300, C + d = 400 d = 200

On Solving a = 300, b = 100, c = 200

(i) x = 4000 – 300 – 200 – 200 = 3300

(ii) y = 2000 – 300 – 200 – 100 = 1400

(iii) z = 1000 – 100 – 200 – 200 = 500

None of these = 10,000 – (3300 + 1400 + 500 + 300+ 100 + 200 + 200)

= 10,000 – 6000

= 4000

12.Two finite sets have m and n elements. The total no. of subsets of the first set is 56 more than the total no. of subsets of second set. Find the value of m and n.

Ans. Let A and B be two sets having m and n elements respectively

no of subsets of A = 2^m

no of subsets of B = 2ⁿ

According to question

2^m = 56 + 2ⁿ

2^m - 2ⁿ = 56

2ⁿ (2^m-n – 1) = 56

2ⁿ (2^m-n – 1) = 2³ (2³ – 1)

2ⁿ = 2³

n = 3

m – n = 3

m – 3 = 3

m = 6