Worksheets – Set Theory  

8 Different Types of Questions on Sets with Answers.

Question (1) Which of the following are sets.

(i) The collection of all good books in a library.

(ii) The collection of all even numbers less than 10.

(iii) The collection of all dishonest people in a village.

(iv) The collection of all students in a school.

(v) The collection of all fat boys in a football team.

(vi) The collection of total of numbers from 10 to 100.

 (vii) The collection of square numbers lying between  100 and 1000.

(viii) The collection of all beautiful toys in a shop.

(ix) The collection of all integer less than 15.

(x) The collection of cube of numbers from 1 to 10.

Answers of question 1, of worksheet on set theory are given below, check correct answers.

(i) Not a set
(ii) Set
(iii) Not a set
(iv) Set
(v) Not a set
(vi) Set
(vii) Set
(viii) Not a set
(ix) Set
(x) Set

Question (2) If,  A = {1, 2, 3, 5, 7}, and B = {4, 9, 6, 10, 8}. Fill the appropriate symbol ∈ or ∉ in the blank place.

  (i) 1 — A

 (ii) 6 — B

(iii) 3 — A

(iv) 5 — B

(v) 15 — A

(vi) 20 — B

(vii) 8 — A

(viii) 7 — A

 (ix) 9 — A

 (x) 10 — B

Answers of question 2, of worksheet on set theory are given below, check correct answers.

(i) 1 ∈ A

(ii) 6 ∈ B

(iii) 3 ∈ A

(iv) 5 ∉ B

(v) 15 ∉ A

(vi) 20 ∉ B

(vii) 8 ∉ A

(viii) 7 ∈ A

(ix) 9 ∉ A

(x) 10 ∈ B

Question (3)  If,  A = {1, 2, 3, 5,}, B = {4, 9, 7, 8} and C = {20, 12, 33, 14, 15},
State whether True or False. 

(i) 2 ∈ A

(ii) 6 ∈ C

(iii) 8 ∈ B

(iv) 10 ∉ B

(v) 14 ∉ A

(vi) 20 ∈ C

(vii) 8 ∈ A

(viii) 7 ∈ A

(ix) 15 ∉ C

(x) 33 ∈ C

Answers of question 3, of worksheet on set theory are given below, check correct answers.

(i) True

(ii) False

(iii) True

(iv) True

(v) True

(vi) True

(vii) False

(viii) False

(ix) True

(x) True 

  

        Now, we see Set builder form worksheet.

Question (4) Write each of the following sets in the set builder form.

(i)   A = { 4, 8, 12, 16, 20}

(ii)  E = { 2, 4, 6, 8, 10}

(iii)  B = {Sunday, Saturday}

(iv) C = {a, e, i, o, u} 

(v) {0, 1, 2, 3, 4, 5, …………30}

(vi) {1, 2, 4, 8, 16}

(vii) D = {a, b, c, d e, f, g…………..x, y, z}

(viii) The set of all natural numbers less than 50.

(ix) The set of all letters in the word Mathematics.

(x) The set of all letters in the word School.

(xi) The set of all Whole numbers lying between 100 and 200.

(xii) {1, 3, 5, 7, 9}

Answers of question 4, of worksheet on set theory are given below, check correct answers.

(i) {x : x is a multiple of 4 and 4 ≤ X ≤ 20}

(ii) {x : x is even numbers and 2 ≤ X ≤ 10}

(iii) {x : x is days of a week beginning with word ‘S’ }

(iv) {x : x is a vowel of the English alphabet}

(v) {x : x ∈ W and 0 ≤ X ≤ 30}

(vi) {x : x is a factor of 16}

(vii) {x : x is letters of the English alphabet}

(viii) {x : x is a natural number and less than 50}

(ix) {x : x is a letter of the word ‘Mathematics’}

(x) {x : x is a letter of the word School}

(xi) {x : x ∈ W and 100 ≤ X ≤ 200}

(xii) {x : x is a odd number and less than 10}

Now, we see Set roster form worksheet.

Question (5) Write each of the following sets in the set roster form.

(i) {x : x is a multiple of 3 and 3 ≤ X ≤ 24} 

(ii) {x : x is a letters in the word algebra.} 

(iii) {x : x is a letters of the word ‘Mathematics’}

(iv) {x : x ∈  N and 3 ≤ X ≤ 8}

(v) The set of all integers lying between -3 and 3. 

(vi) {x : x is a vowel of the English alphabet}

(vii) {x : x is even number and less than 11}

 (viii) {x : x  N, and 3< x < 7}

(ix) The set of all vowels in the word Mathematics.

(x) {x : x is perfect square, and 16< x < 81}

(xi) {x : x is perfect cube, and 27< x < 125}

(xii) A= {x : x is positive integer and divisor of 32}

(xiii)  The set of all factors of 10.

Answers of question 5, of worksheet on set theory are given below, check correct answers.

(i) {3, 6, 9, 12, 15, 18, 21, 24}

(ii) {a, l, g, e, b, r}

(iii) {m, a, t, h, e, i, c, s}

(iv) {3, 4, 5, 6, 7, 8}

(v) {-2, -1, 0, 1, 2}

(vi) {a, e, i, o, u}

(vii) {2, 4, 6, 8, 10}

(viii) {4, 5, 6,}

(ix) {a, e, i}

(x) {25, 36, 49, 64}

(xi) {64}

(xii) {4, 8, 16}

(xiii) {2, 5}

Question (6) Select each of the following sets in finite and infinite sets.

Answers of question 6, of worksheet on set theory are given below, check correct answers.

(i)Infinite 
(ii)Infinite
(iii)Infinite
(iv)Infinite
(v) Finite
(vi) Infinite
(vii) Finite
(viii) Finite
(ix) Finite

Question (7) Which of the following sets are equal sets.

(1)  (i)  A = {p, q, r, s}       (ii) B =  {r, s, t, u} 

(2)  (i)  A = {a, b, c, d, e} (ii)  B = {d, c, a, e, b}

(3)  (i)  A = {1, 3, 5, 7, 9}       (ii)  B = {x : x is a odd positive integer x ≤ 9}

(4)  (i)  A = {2, 4, 6, 8, 10} and      (ii)  B = {x : x is a even positive integer x ≤ 10}

(5) (i)   A = {The set of letters in the word Object} 
     (ii)  A = {The set of letters in the word Subject}

 (6)  (i)  A = {2, -1, 3}         (ii) B = {-3, -1, 2} 

 (7)  (i)  A = {0, -5, 4}         (ii) B = {-5, 1, 0}

 Answers of question 7, of worksheet on set theory are given below, check correct answers.

(1) Not equal

(2) equal

(3) equal

(4) equal

(5) Not equal

(6) Not equal

(7) Not equal

Question (8) Which of the following sets are equivalent sets.

(1)  (i)  A = {p, q, r, s}       (ii) B =  {a, b, t, u}

(2)  (i)  A = {p, q, r, s}       (ii) B =  {r, s, q, p}

(3) (i) A = {The set of letters in the word boot} 
     (ii) A = {The set of letters in the word book}

(4) (i) A =The set of days in a week.     (ii) B =  {1, 2, 3, 4, 5, 6, 7}

(5) (i) A =The set of months in a year.     (ii) B =  {1, 2, 3, 4, 5, 6,}

(6)  (i)  A = {p, q, r, s ,t}       (ii) B =  {r, s, q, p}

(7)  (i)  A = {2, 4, 6, 8 ,}        (ii) B =  {4, 2, 6, 10, 8}

Answers of question 8, of worksheet on set theory are given below, check correct answers.

(1) equivalent

(2) equivalent

(3) equivalent

(4) equivalent

(5) Not equivalent

(6) Not equivalent

(7) Not equivalent