Worksheet on Set

In worksheet on set we will solve 12 different types of questions. The questions on sets are basically related on elements of set and notation of a set, representation of a set, cardinal number of a set, and also types and pairs of set.

1. Which of the following are sets? Justify your answer.

(a) The collection of all the days in a week beginning with the letter ‘T’.

(b) The collection of all difficult questions in the chapter on sets.

(c) The collection of girls in your class.

(d) The collection of all rivers in India.

(e) The collection of all active teachers in the school.

(f) The collection of all integers more than -3.

(g) The collection of all beautiful flowers in the park.


2. If,

A = {3, 5, 7, 9}

B = {2, 4, 6, 8, 10}

C = {12, 14, 18, 20, 24}

D = {21, 26, 31, 36}

(a) State whether true or false.

(i) 13 ∈ C

(ii) 6 ∉ A

(iii) 9 ∉ A

(iv) 24 ∈ C

(v) 31 ∈ D

(vi) 36 ∉ D

(vii) 20 ∉ C

(viii) 9 ∈ A


(b) Fill in the blanks.

(i) 3 ∈ ___

(ii) 4 ___ B

(iii) 26 ___ C

(iv) 8 ∈ ___

(v) 5 ___ A

(vi) 6 ___ C

(vii) 21 ___ D

(viii) 18 ___ B


3. Write the following sets in the roster form.

(a) A = The set of all even numbers less than 12

(b) B = The set of all prime numbers greater than 1 but less than 29

(c) C = The set of integers lying between -2 and 2

(d) D = The set of letters in the word LOYAL

(e) E = The set of vowels in the word CHOICE

(f) F = The set of all factors of 36

(g) G = {x : x ∈ N, 5 < x < 12}

(h) H = {x : x is a multiple of 3 and x < 21}

(i) I = {x : x is perfect cube 27 < x < 216}

(j) J = {x : x = 5n - 3,n ∈ W, and n < 3}

(k) M = {x : x is a positive integer and x2 < 40}

(l) N = {x : x is a positive integer and is a divisor of 18}

(m) P = {x : x is an integer and x + 1 = 1}

(n) Q = {x : x is a color in the rainbow}


4. Write each of the following in set builder form.

(a) A = {5, 10, 15, 20}

(b) B = {l, 2, 3, 6, 9, 18}

(c) C = {P, R, I, N, C, A, L}

(d) D = {0}

(e) E = { }

(f) F = {0, 1, 2, 3, ......, 19}

(g) G = {—8, —6, —4, —2}

(h) H = {Jan, June, July}

(i) I = {a, e, i, 0, u}

(j) J = {a, b, c, d, …..., z}

(k) K = {1/1, 1/2, 1/3, 1/4, 1/5, 1/6}

(l) L = {1, 3, 5, 7, 9}


5. Write the cardinal number for each of the following.

(a) X = The set of months in a year

(b) Y = The set of letters in the word INTELLIGENT

(c) Z = The set of prime numbers from 2 to 11

(d) P = {x : x is an even prime number}

(e) Q = {x : x is a quadrilateral having 5 sides}

(f) R = {x : x ∈ I, -5 < x < 2}

(g) S = {x | x ∈ W, x + 2 < 9}

(h) T = {x | x is a prime number which is a divisor of 60}

(i) V = {x : x is a 2-digit number such that the sum of digits is 6}

(j) W = The set of hours in a day


6. Classify the following as finite and infinite sets.

(a) A = {x : x ∈ N and x is even}

(b) B = {x : x ∈ N and x is composite}

(c) C = {x : x ∈ N and 3x -2 = 0}

(d) D = {x : x ∈ N and x2 = 9}

(e) E = {The set of numbers which are multiples of 3}

(f) G = {The set of letters in the English alphabet}

(g) H = {The set of persons living in a house}

(h) I = {x | x ∈ I, x < -2}

(i) J = {x | x ∈ P, p is a prime number}

(I) K = The set of fractions with numerator 3.


7. Identify the following as null set or singleton set.

(a) A = {x | x ∈ N, 1 < x < 2}

(b) P = {Point of intersection of two lines}

(c) C = {x : x is an even prime number greater than 2}

(d) Q = {x | x is an even prime number}

(e) E = {x : x2 = 9, x is even}

(f) R = {The set of whole numbers lying between 0 and 2}

(g) B = {0}

(h) D = {The set of largest 1 digit number}

(i) F = {The set of triangles having 4 sides}

(j) H = {The set of even numbers not divisible by 2}


8. From the sets given below, select the equal sets.

A = {3, 5, 9, 13}

B = {2, 3, 4, 5}

C = {5, 9, 13, 15}

D = {4, 2, 5, 3}

E = {-2, 2}

F = {o, b}

G = {2, -2}

H = {1, 2}


9. Are two sets A and B equal? Give reasons to support your answer.

(a) A = {x : x is a letter in the word SEAT}

     B = {x : x is a letter in the word TASTE}

(b) A = {2, 6, 10, 14}

     B = {6, 2, 14, 16}

(c) A = {1, 3, 5, 7, 9}

     B = {x : x is a positive odd integer x ≤ 9}

(d) A = {0}

     B = {x : x > 15 and x < 5}


10. Which of the following pairs of sets are equivalent or equal?

(a) A = {x : x ∈ N, x ≤ 6}

     B = {x : x ∈ W, 1 ≤ x ≤ 6}

(b) P = {The set of letters in the word ‘plane’}

     Q = {The set of letters in the word ‘plain’}

(c) X = {The set of colors in the rainbow)

     Y = {The set of days in a week}

(d) M = {4, 8, 12, 16}

     N = {8, 12, 4, 16}

(e) A = {x | x ∈ N, x ≤ 5}

     B = {x | x ∈ I, 5 < x ≤ 10}


11. Find which of the following sets are disjoint or overlapping.

(a) A = {The set of boys in the school}

     B = {The set of girls in the school}

(b) P = {The set of letters in the English alphabet}

    Q = {The set of vowels in the English alphabet}

(c) X = {x : x is an odd number, x < 9}

    Y = {x : x is an even number, x < 10}

(d) M = {x : x is a factor of 24}

     N = {x : x is a multiple of 3, less than 30}

(e) E = {9, 99, 999}

     F = {1, 10, 100}

(f) G = {The set of letters in the word TAME}

    H = {The set of letters in the word MATE}


12. State whether the following are true or false.

(a) The set of letters in the word MASTER is finite.

(b) The set of vowels in the word PLANET is an empty set.

(c) {0} represents a null set.

(d) Equivalent sets are always equal.

(e) An empty set is a finite set.

(f) 10 ∉ set of multiples of 5.

(g) 4 ∈ {x : 4 ≤ x ≤ 10}

(h) If two sets are equal, they are also equivalent.

(i) If P = {x : x = 2n, n ∈ N}

Q = {x : x 2n + 1, n ∈ N}

then P and Q are disjoint sets

Answers for worksheet on set theory are given below to make sure that the answers are correct.


Answers:

1. (a), (c), (d) and (f) are sets.
Since they are well-defined collection of distinct objects.


2. (a) (i) False
(ii) True
(iii) False
(iv) True
(v) True
(vi) False
(vii) False
(viii) True

(b) (i) A
(ii) Є
(iii) ∉
(iv) B
(v) Є
(vi) ∉
(vii) Є
(viii) ∉


3. (a) {2, 4, 6, 8, 10}
(b) {2, 3, 5, 7, 11, 13, 17, 19, 23}
(c) {-1, 0, 2}
(d) {L, O, Y, A}
(e) {O, I, E}
(f) {1, 2, 3, 4, 6, 9, 12, 18, 36}
(g) {6, 7, 8, 9, 10, 11}
(h) {3, 6, 9, 12, 15, 18}
(i) {64, 125}
(j) {-3, 2, 7}
(k) {1, 2, 3, 4, 5, 6}
(l) {1, 2, 3, 6, 9, 18}
(m) {O}
(n) {red, orange, yellow, green, blue, indigo, violet}


4. (a) {x : x is a multiple of 5 and 5 ≤ x ≤ 20}
(b) {x : x is a factor of 18}
(c) {x : x is a letter of the word ‘Principal’}
(d) {x : x ∊ W and x < 1}
(e) {x : x ∊ N and x < 1)
(f) {x : x ∊ W and 0 ≤ x ≤ 19}
(g) {x : x = -2n and n ∊ N and 1 ≤ n ≤ 4}
(h) {x : x is a month of the year beginning with J}
(i) {x : x is a vowel of the English alphabet}
(j) {x : x is a letter of the English alphabet}
(k) {x : x = 1/x, n ∊ N and 1 ≤ n ≤ 6}
(l) {x : x is odd, x ≤ 9}


5. (a) 12
(b) 6
(c) 5
(d) 1
(e) 0
(f) 6
(g) 7
(h) 3
(i) 6
(j) 24


6. (a) infinite
(b) infinite
(c) finite
(d) finite
(e) infinite
(f) finite
(g) finite
(h) finite
(i) infinite
(j) infinite
(k) infinite


7. (a) null
(b) singleton
(c) null
(d) singleton
(e) null
(f) singleton
(g) singleton
(h) singleton
(i) null
(j) null


8. B = D and E = G


9. Equal sets (a), (c) Elements same


10. Equal sets (a), (d)
Equivalent sets (b), (c), (e)


11. Disjoint sets (a), (c), (e)
Overlapping sets (b), (d), (f)


12. (a) True
(b) True
(c) False
(d) False
(e) False
(f) True
(g) False
(h) True
(i) True
(j) True

Sets and Venn-diagrams Worksheets

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Worksheet on Properties of a Set

Worksheet on Sets in Roster Form

Worksheet on Sets in Set-builder Form

Worksheet on Finite and Infinite Sets

Worksheet on Equal Sets and Equivalent Sets

Worksheet on Empty Sets

Worksheet on Subsets

Worksheet on Union and Intersection of Sets

Worksheet on Disjoint Sets and Overlapping Sets

Worksheet on Difference of Two Sets

Worksheet on Operation on Sets

Worksheet on Cardinal Number of a Set

Worksheet on Venn Diagrams



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