Union of Sets using Venn Diagram

Learn how to represent the union of sets using Venn diagram. The union set operations can be visualized from the diagrammatic representation of sets.

The rectangular region represents the universal set U and the circular regions the subsets A and B. The shaded portion represents the set name below the diagram.

Let A and B be the two sets. The union of A and B is the set of all those elements which belong either to A or to B or both A and B.

Now we will use the notation A U B (which is read as ‘A union B’) to denote the union of set A and set B.

Thus, A U B = {x : x ∈ A or x ∈ B}.

Clearly, x ∈ A U B   

⇒ x ∈ A or x ∈ B

Similarly, if x ∉ A U B  

⇒ x ∉ A or x ∉ B

Therefore, the shaded portion in the adjoining figure represents A U B.

Union of Sets using Venn Diagram

Thus, we conclude from the definition of union of sets that A ⊆ A U B, B ⊆ A U B.


From the above Venn diagram the following theorems are obvious:

(i) A ∪ A = A                        (Idempotent theorem)

(ii) A ⋃ U = U                       (Theorem of ⋃) U is the universal set.

(iii) If A ⊆ B, then A ⋃ B = B

(iv) A ∪ B = B ∪ A                (Commutative theorem)

(v) A ∪ ϕ = A                      (Theorem of identity element, is the identity of ∪) 

(vi) A ⋃ A' = U                     (Theorem of ⋃) U is the universal set.


Notes:

A ∪ ϕ = ϕ ∪ A = A i.e. union of any set with the empty set is always the set itself.


Solved examples of union of sets using Venn diagram:

1. If A = {2, 5, 7} and B = {1, 2, 5, 8}. Find A U B using venn diagram.

Solution:

According to the given question we know, A = {2, 5, 7} and B = {1, 2, 5, 8}

Now let’s draw the venn diagram to find A union B.

Union using Venn Diagram

Therefore, from the Venn diagram we get A U B = {1, 2, 5, 7, 8}


2. From the adjoining figure find A union B.

Find A union B

Solution:

According to the adjoining figure we get;

Set A = {0, 1, 3, 5, 8}

Set B = {2, 5, 8, 9}

Therefore, A union B is the set of elements which in set A or in set B or in both.

Thus, A U B = {0, 1, 2, 3, 5, 8, 9}

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 Union of Sets using Venn Diagram to HOME PAGE


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.



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.



Share this page: What’s this?

Recent Articles

  1. 4th Grade Mental Math on Roman Numerals | Roman Numerals Quiz

    Feb 23, 24 03:55 PM

    In 4th grade mental math on numbers, students can practice different questions on write the Hindu-Arabic numerals, write the Roman Numerals, comparison of roman numerals, addition of roman numerals.

    Read More

  2. 4th Grade Mental Math on Numbers | Mental Math 4th Grade with Answers

    Feb 23, 24 02:24 PM

    4th Grade Mental Math on Numbers
    In 4th grade mental math on numbers, students can practice different questions on numbers in figures, number name, place value, face value, comparison of number and formation of greatest and smallest…

    Read More

  3. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 23, 24 01:28 PM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More

  4. Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

    Feb 22, 24 04:15 PM

    Roman Numbers Table
    Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) V…

    Read More

  5. Roman Symbols | What are Roman Numbers? | Roman Numeration System

    Feb 22, 24 02:30 PM

    Roman Numbers
    Do we know from where Roman symbols came? In Rome, people wanted to use their own symbols to express various numbers. These symbols, used by Romans, are known as Roman symbols, Romans used only seven…

    Read More