Problems on Operation on Sets

Solved problems on operation on sets are given below to get a fair idea how to find the union and intersection of two or more sets.


We know, the union of sets is a set which contains all the elements in those sets and intersection of sets is a set which contains all the elements that are common in those sets.

Click Here to know more about the two basic operations on sets.


Solved problems on operation on sets:

1. If A = {1, 3, 5}, B = {3, 5, 6} and C = {1, 3, 7} 

(i) Verify that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

(ii) Verify A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Solution:

(i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

L.H.S. = A ∪ (B ∩ C)

B ∩ C = {3}

A ∪ (B ∩ C) = {1, 3, 5} ∪ {3} = {1, 3, 5} ……………….. (1)

R.H.S. = (A ∪ B) ∩ (A ∪ C)

A ∪ B = {1, 3, 5, 6}

A ∪ C = {1, 3, 5, 7}

(A ∪ B) ∩ (A ∪ C) = {1, 3, 5, 6} ∩ {1, 3, 5, 7} = {1, 3, 5}     ……………….. (2)

From (1) and (2), we conclude that;

A ∪ (B ∩ C) = A ∪ B ∩ (A ∪ C)  [verified]

(ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

L.H.S. = A ∩ (B ∪ C)

B ∪ C = {1, 3, 5, 6, 7}

A ∩ (B ∪ C) = {1, 3, 5} ∩ {1, 3, 5, 6, 7} = {1, 3, 5}     ……………….. (1)
R.H.S. = (A ∩ B) ∪ (A ∩ C)

A ∩ B = {3, 5}

A ∩ C = {1, 3}

(A ∩ B) ∪ (A ∩ C) = {3, 5} ∪ {1, 3} = {1, 3, 5}     ……………….. (2)

From (1) and (2), we conclude that;

A ∩ (B ⋃ C) = (A ∩ B) ⋃ (A ∩ C)  [verified]

More worked-out problems on operation on sets to find the union and intersection of three sets.

2. Let A = {a, b, d, e}, B = {b, c, e, f} and C = {d, e, f, g}

(i) Verify A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

(ii) Verify A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Solution:

(i) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

L.H.S. = A ∩ (B ∪ C)

B ∪ C = {b, c, d, e, f, g}

A ∩ (B ∪ C) = {b, d, e}     ……………….. (1)

R.H.S. = (A ∩ B) ∪ (A ∩ C)

A ∩ B = {b, e}

A ∩ C = {d, e}

(A ∩ B) ∪ (A ∩ C) = {b, d, e}     ……………….. (2)

From (1) and (2), we conclude that;

A ∩ (B ⋃ C) = (A ∩ B) ⋃ (A ∩ C)  [verified]

(ii) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

L.H.S. = A ∪ (B ∩ C)

B ∩ C = {e, f}

A ∪ (B ∩ C) = {a, b, d, e, f}     ……………….. (1)

R.H.S. = (A ∪ B) ∩ (A ∪ C)

A∪B = {a, b, c, d, e, f}

A∪C = {a, b, d, e, f, g}

(A ∪ B) ∩ (A ∪ C) = {a, b, d, e, f}     ……………….. (2)

From (1) and (2), we conclude that;

A ∪ (B ∩ C) = A ∪ B ∩ (A ∪ C)  [verified]

Set Theory

Sets Theory

Representation of a Set

Types of Sets

Finite Sets and Infinite Sets

Power Set

Problems on Union of Sets

Problems on Intersection of Sets

Difference of two Sets

Complement of a Set

Problems on Complement of a Set

Problems on Operation on Sets

Word Problems on Sets

Venn Diagrams in Different Situations

Relationship in Sets using Venn Diagram

Union of Sets using Venn Diagram

Intersection of Sets using Venn Diagram

Disjoint of Sets using Venn Diagram

Difference of Sets using Venn Diagram

Examples on Venn Diagram








8th Grade Math Practice

From Problems on Operation on Sets 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. Intersecting Lines | What Are Intersecting Lines? | Definition

    Jun 14, 24 11:00 AM

    Intersecting Lines
    Two lines that cross each other at a particular point are called intersecting lines. The point where two lines cross is called the point of intersection. In the given figure AB and CD intersect each o…

    Read More

  2. Line-Segment, Ray and Line | Definition of in Line-segment | Symbol

    Jun 14, 24 10:41 AM

    Line-Segment, Ray and Line
    Definition of in Line-segment, ray and line geometry: A line segment is a fixed part of a line. It has two end points. It is named by the end points. In the figure given below end points are A and B…

    Read More

  3. Definition of Points, Lines and Shapes in Geometry | Types & Examples

    Jun 14, 24 09:45 AM

    How Many Points are There?
    Definition of points, lines and shapes in geometry: Point: A point is the fundamental element of geometry. If we put the tip of a pencil on a paper and press it lightly,

    Read More

  4. Subtracting Integers | Subtraction of Integers |Fundamental Operations

    Jun 13, 24 04:32 PM

    Subtraction of Integers
    Subtracting integers is the second operations on integers, among the four fundamental operations on integers. Change the sign of the integer to be subtracted and then add.

    Read More

  5. 6th Grade Worksheet on Whole Numbers |Answer|6th Grade Math Worksheets

    Jun 13, 24 04:17 PM

    6th Grade Worksheet on Whole Numbers
    In 6th Grade Worksheet on Whole Numbers contains various types of questions on whole numbers, successor and predecessor of a number, number line, addition of whole numbers, subtraction of whole number…

    Read More