SUBSETS WORKSHEET

About "Subsets worksheet"

Subsets worksheet is much useful to the students who woulds like to practice problems on set theory. 

Subsets worksheet - Problems

1)  Let A  =  {1, 2, 3, 4, 5} and B  =  { 5, 3, 4, 2, 1}. Determine whether B is a proper subset of A. 

2)  Let A  =  {1, 2, 3, 4, 5} and B  =  {1, 2, 5}. Determine whether B is a proper subset of A. 

3)  Let A  =  {1, 2, 3, 4, 5} find the number of proper subsets of A. 

4)  Let A  =  {1, 2, 3 } find the power set of A.

5)  Let A  =  {a, b, c, d, e} find the cardinality of power set of A.

Subsets worksheet - Answers

Problem 1 :

Let A  =  {1, 2, 3, 4, 5} and B  =  { 5, 3, 4, 2, 1}. Determine whether B is a proper subset of A. 

Solution : 

If B is the proper subset of A, every element of B must also be an element of A and also B must not be equal to A. 

In the given sets A and B, every element of B is also an element of A. But B is equal A.

Hence, B is the subset of A, but not a proper subset. 

Let us look at the next problem on "Subsets worksheet"

Problem 2 :

Let A  =  {1, 2, 3, 4, 5} and B  =  {1, 2, 5}. Determine whether B is a proper subset of A. 

Solution : 

If B is the proper subset of A, every element of B must also be an element of A and also B must not be equal to A. 

In the given sets A and B, every element of B is also an element of A.

And also But B is not equal to A.

Hence, B is a proper subset of A. 

Let us look at the next problem on "Subsets worksheet"

Problem 3 :

Let A  =  {1, 2, 3, 4, 5} find the number of proper subsets of A. 

Solution : 

Let the given set contains "n" number of elements.

Then, the formula to find number of proper subsets is

=  2ⁿ¹

The value of "n" for the given set  A is "5".

Because the set A =  {1, 2, 3, 4, 5} contains "5" elements. 

Number of proper subsets  =  2¹

=  2

=  16

Hence, the number of proper subsets of A is 16.

Let us look at the next problem on "Subsets worksheet"

Problem 4 :

Let A  =  {1, 2, 3 } find the power set of A.

Solution : 

We know that the power set is the set of all subsets.

Here, the given set A contains 3 elements.

Then, the number of subsets  =  2³  =  8

Therefore, 

P(A) =  { {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, {1, 2, 3}, { } }

Let us look at the next problem on "Subsets worksheet"

Problem 5 :

Let A  =  {a, b, c, d, e} find the cardinality of power set of A

Solution : 

The formula for cardinality of power set of A is given below. 

n[P(A)]  =  2ⁿ

Here "n" stands for the number of elements contained by the given set A. 

The given set A contains "5" elements. So n = 5. 

Then, we have 

n[P(A)]  =  2

n[P(A)]  =  32

Hence, the cardinality of the power set of A is 32. 

Apart from "Subsets worksheet", let us look at some other worksheets on "Set theory"

Description of sets worksheet

1. Which of the following are sets ? 

(i)  The collection of good books

(ii)  The collection of prime numbers less than 30

(iii)  The collection of ten most talented mathematics teachers.

(iv)  The collection of all students in your school

(v)  The collection of all even numbers

2.  Let A = {0, 1, 2, 3, 4, 5}. Insert the appropriate symbol  or  in the blank spaces.

(i) 0 ----- A

(ii) 6 ----- A

(iii) 3 ----- A

(iv) 4 ----- A

(v) 7 ----- A

Description of sets worksheet - Answers

1) Answers 

(i)  Not a set

(ii)  Set

(iii)  Not a set

(iv)  Set

(v)  Set

2) Answers

(i)  0  A

(ii)  6  A

(iii)  3 ∈ A

(iv)  4 ∈ A

(v)   7 ∉ A

Set builder form worksheet

Write the following sets in Set-Builder form

(i)  The set of all positive even numbers

(ii)  The set of all whole numbers less than 20

(iii)  The set of all positive integers which are multiples of 3

(iv)  The set of all odd natural numbers less than 15

(v)  The set of all letters in the word ‘computer’

Set builder form worksheet - Answers

(i)  {x : x is a positive even number}

(ii)  {x : x is a whole number and x < 20}

(iii)  {x : x is a positive integer and multiple of 3}

(iv)  {x : x is an odd natural number and x < 15}

(v)   {x : x is a letter in the word 'computer'}

Roster form worksheet

Write the following sets in Roster form

1)  A  =  { x : x ∈ N, 2 < x ≤ 10 }

2)  B  =  { x : x ∈ Z, (-1/2) < x < 11/2 }

3)  C  =  {x : x is a prime number and a divisor of 6 }

4)  D  =  { x : x = 2ⁿ, n ∈ N and n ≤ 5 }

5)  E  =  { x : x = 2y - 1, y ≤ 5 y ∈ W }

6)  F  =  {  x : x is an integer, x² ≤ 16 }

Roster form worksheet - Answers

1)  A = { 3, 4, 5, 6, 7, 8, 9, 10 }

2)  B =  { 0, 1, 2, 3, 4, 5 }

3)  C  =  { 2, 3 }

4)  D  =  { 2, 4, 8, 16, 32 }

5)  E  =  { -1, 1, 3, 5, 7, 9 }

6)  F  =  {  -4, -3, -2, -1, 0, 1, 2, 3, 4 }

Descriptive form of set worksheet

Write the following sets in Descriptive form

(i)  A  =  {a, e, i, o, u}

(ii)  B  =  {1, 3, 5, 7, 9, 11}

(iii)  C  =  {1, 4, 9, 16, 25}

(iv)  P  =  {x : x is a letter in the word ‘set theory’}

(v)  Q  =  {x : x is a prime number between 10 and 20} 

Descriptive form of set worksheet - Answers

(i)  A is the set of all vowels in the English alphabet

(ii)  B is the set of all odd natural numbers less than or equal to 11

(iii)  C is the set of all square numbers less than 26.

(iv)  P is the set of all letters in the word ‘set theory’

(v)  Q is the set of all prime numbers between 10 and 20

Sets word problems worksheet

1)  In a survey of university students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry, 22 had taken chemistry and physics course, and 14 had taken all the three courses. Find how many had taken one course only.

2)  In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the total number of students in the group. (Assume that each student in the group plays at least one game.)

3)  In a class of 60 students, 40 students like math, 36 like science, 24 like both the subjects. Find the number of students who like

(i) Math only, (ii) Science only  (iii) Either Math or Science (iv) Neither Math nor science

Sets word problems worksheet - Answers

Answer for question (1) :

Step 1 :

Venn diagram related to the information given in the question: 

Step 2 :

From the venn diagram above, we have

No. of students who had taken only math = 24

No. of students who had taken only chemistry = 60

No. of students who had taken only physics = 22

Step 3 :

Total no. of students who had taken only one course

                                  = 24 + 60 + 22

                                 = 106

Hence, the total number of students who had taken only one course is 106

Answer for question (2) :

Step 1 :

Venn diagram related to the information given in the question:

Step 2 :

Total number of students in the group

                                =  28 + 12 + 18 + 7 + 10 + 17 + 8

                                = 100

Hence, the total number of students in the group is 100

Answer for question (3) :

Step 1 :

Let M and S represent the set of students who like math and science respectively.

Step 2 :

From the information given in the question, we have

n(M) = 40, n(S) = 36, n(MnS) = 24

Step 3 :

Answer (i) : No. of students who like math only

                                   = n(M) - n(MnS)

                                   = 40 - 24

                                  = 16

Step 4 :

Answer (ii) : No. of students who like science only

                                   = n(S) - n(MnS)

                                   = 36 - 24

                                  = 12

Step 5 :

Answer (iii) : No. of students who like either math or science

                                  = n(M or S) 

                                  = n(MuS) 

                                  = n(M) + n(S) - n(MnS)

                                  = 40 + 36 - 24

                                  = 52

Step 6 :

Answer (iv) :

Total no. students who like any of the two subjects = n(MuS) = 52

No. of students who like neither math nor science

                                         = 60 - 52

                                         = 8

After having gone through the stuff given above, we hope that the students would have understood "Subsets worksheet". 

Apart from the stuff given above, if you want to know more about "Subsets worksheet", please click here

Apart from the stuff, "Subsets worksheet", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

ALGEBRA

Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power

COMPETITIVE EXAMS

Quantitative aptitude

Multiplication tricks

APTITUDE TESTS ONLINE

Aptitude test online

ACT MATH ONLINE TEST

Test - I

Test - II

TRANSFORMATIONS OF FUNCTIONS

Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices

ORDER OF OPERATIONS

BODMAS Rule

PEMDAS Rule

WORKSHEETS

Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet

TRIGONOMETRY

SOHCAHTOA

Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem

MENSURATION

Mensuration formulas

Area and perimeter

Volume

GEOMETRY

Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem

ANALYTICAL GEOMETRY

Analytical geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance

Midpoint

Area of triangle

Area of quadrilateral

Parabola

CALCULATORS

Matrix Calculators

Analytical geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator

MATH FOR KIDS

Missing addend 

Double facts 

Doubles word problems

LIFE MATHEMATICS

Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work

SYMMETRY

Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry

CONVERSIONS

Converting metric units

Converting customary units

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6