Worksheet on Set Theory

In worksheet on set theory we will solve 10 different types of questions. The questions on sets are basically related on sets and their representation and also methods of representing a set.

1. Which of the following are well-defined sets?

(a) All the colors in the rainbow. 

(b) All the points that lie on a straight line. 

(c) All the honest members in the family. 

(d) All the consonants of the English alphabet. 

(e) All the tall boys of the school. 

(f) All the efficient doctors of the hospital. 

(g) All the hardworking teachers in a school. 

(h) All the prime numbers less than 100. 

(i) All the letters in the word GEOMETRY. 

2. Let A = (a, b, c, d, e, f}. Insert the appropriate symbol ∈ or βˆ‰ in the blank space.

(a) d __ A

(b) y __ A

(c) m __ A

(d) a __ A

(e) e __ A

(f) x __ A

Worksheet on Set Theory
3. Write the following sets in the set builder form.

(a) A = {2, 4, 6, 8}

(b) B = {3, 9, 27, 81}

(c) C = {1, 4, 9, 16, 25}

(d) D = {1, 3, 5, ......}

(e) E = {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ......., 52}

(f) F = {-10, ......, -3, -2, -1, 0, 1, 2, …..., 5}

(g) G = {O}

(h) P = { }

(i) H = {-5, 5}

(j) Q = {V, I, B, G, Y, 0, R}


4. Write the following sets in the roster form.

(a) A = {x : x ∈ W, x ≀ 5}

(b) B = {x : x ∈ I, -3 < x < 3)

(c) C = {x : x is divisible by 12}

(d) D = {x : x = 3p, p ∈ W, p ≀ 3}

(e) E = {x : x = a2, a ∈ N, 3 < a < 7}

(f) F = {x : x = n/(n + 1), n ∈ N and n ≀ 4}

(g) G = {x : x ∈ N, 3x - 2 < 5}

(h) J = {x : x ∈ N, x2 < 16}

(i) K = {x : x is a prime number which is a divisor of 42}

(j) H = {x : x is a 2-digit natural number such that the sum of its digits is 5}


5. Which of the following are the examples of an empty set?

(a) The set of even natural numbers divisible by 3.

(b) The set of all prime numbers divisible by 2.

(c) {x : x ∈ N, 5 < x < 6}

(d) The set of odd natural numbers divisible by 2.

(e) B = {O}

(f) C = { }

(g) D = {x : x ∈ R, x2 = -1}

(h) E = {x : x ∈ W, 3x + 1 = 2}

(i) P = {x : x is a prime number, 54 < x < 58}

(j) Q = {x : x = 2n + 3, n ∈ W, n ≀ 5}

Worksheet on Set Theory
6. Classify the following as finite and infinite sets.

(a) The set of days in a week

(b) A = {x : x ∈ N x > 1}

(c) B = {x : x is an even prime number}

(d) C = {x : x is a multiple of 5}

(e) D = {x : x is a factor of 30}

(f) P = {x : x ∈ Z, x < -1}

(g) The set of all letters in the English alphabet

(h) The set of all real numbers


7. From the sets given below, identify the equal sets.

A = {3, 5, 9, 11}         Q = {m, s, t} 

B = {8, 9, 1, 13}         R = {o, p, a, z} 

C = {-3, 3}           T = {1, 8, 9, 13}

D = {s, t, m}           M = {3, -3} 

P = {9, 3, 5, 11} 

X = {a, o, z, p}


8. Are the following pairs of sets equal?

(a) A = {2}           B = {x : x ∈ N, x is an even prime number}.

(b) P = {1, 4, 9}         Q = {x : x = n2, n ∈ N, n ≀ 3) 

(c) X = {x : x ∈ W, x < 5}       Y = {x : x ∈ N, x ≀ 5} 

(d) M = {a, b, c, d}         N = {p, q, r, s}

(e) D = {x : x is a multiple of 30}     E = {x : x is a factor of 10}



Worksheet on Set Theory
9. Which of the following are equivalent sets?

(a) A = {1, 2, 3}           B = {4, 5} 

(b) P = {q, s, m}           Q = {6, 9, 12} 

(c) X = {x : x is a prime number less than 10}       Y = {x : x ∈ N, x ≀ 4}

(d) R = {x : x = 2n + 3, n < 4, n ∈ N}      S = {x : x = n/(n + 1), n ∈ R, n ≀ 4} 

(e) The set of vowels in the English alphabet 

(f) The set of consonants in the English alphabet


10. Find the cardinal number of the following sets.

(a) A = {x : x ∈ I, 2 < x < 7} 

(b) B = {x : n ∈ N, x = n2, n < 3}

(c) The set of months in a year 

(d) C = {x : x ∈ Z+, x < 100}

(e) D = {x : x = n3, n ∈ W, n < 5} 

(f) The set of letters in the word MALAYALAM


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


Answers:


1. (a), (b), (d), (h), (i) 

2. (a) ∈

(b) βˆ‰

(c) βˆ‰

(d) ∈

(e) ∈

(f) βˆ‰

3. (a) {x : x is even and x ≀ 8}

(b) {x : x = 3n, n ∈ N, n ≀ 4}

(c) {x : x = n2, n ≀ 5, n ∈ N}

(d) {x : x is odd}

(e) {x : x is even, 4 ≀ x ≀ 52 and y : y = 3(2m + 1), 1 ≀ m ≀ 8}

(f)

Worksheet on Set Theory

● Sets and Venn-diagrams - Worksheets

● Worksheet on Set Theory

● Worksheet on Elements of a Set

● Worksheet on Representation on Set

● Worksheet on Set Operations

● Worksheet to Find the Cardinal Number of the Sets

● Worksheet on Cardinal Properties of Sets

● Worksheet on Sets using Venn Diagram

● Worksheet on Union and Intersection using Venn Diagram



8th Grade Math Practice

Math Home Work Sheets

From Worksheet on Set Theory to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Area, Perimeter and Volume | Square, Rectangle, Cube,Cubo

    Jul 28, 25 01:52 PM

    Volume of a Cuboids
    In this worksheet on area perimeter and volume you will get different types of questions on find the perimeter of a rectangle, find the perimeter of a square, find the area of a rectangle, find the ar…

    Read More

  2. Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox

    Jul 25, 25 03:15 AM

    Volume of a Cube and Cuboid
    We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:

    Read More

  3. Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume

    Jul 24, 25 03:46 PM

    Volume of Cuboid
    Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measur…

    Read More

  4. Volume of a Cube | How to Calculate the Volume of a Cube? | Examples

    Jul 23, 25 11:37 AM

    Volume of a Cube
    A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure i…

    Read More

  5. 5th Grade Volume | Units of Volume | Measurement of Volume|Cubic Units

    Jul 20, 25 10:22 AM

    Cubes in Cuboid
    Volume is the amount of space enclosed by an object or shape, how much 3-dimensional space (length, height, and width) it occupies. A flat shape like triangle, square and rectangle occupies surface on…

    Read More