Intersection of Sets using Venn Diagram

Learn how to represent the intersection of sets using Venn diagram. The intersection 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 intersection of A and B is the set of all those elements which belong to both A and B.

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

Thus, A ∩ B = {x : x ∈ A and x ∈ B}.

Clearly, x ∈ A ∩ B   

⇒ x ∈ A and x ∈ B

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

Intersection of Sets using Venn Diagram

Thus, we conclude from the definition of intersection of sets that A ∩ B ⊆ A, A ∩ B ⊆ B.


From the above Venn diagram the following theorems are obvious:

(i) A ∩ A = A                        (Idempotent theorem) 

(ii) A ∩ U = A                       (Theorem of union) 

(iii) If A ⊆ B, then A ∩ B = A.

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

(v) A ∩ ϕ = ϕ                       (Theorem of ϕ) 

(vi) A ∩ A’ = ϕ                      (Theorem of ϕ) 

The symbols ⋃ and ∩ are often read as ‘cup’ and ‘cap’ respectively.

For two disjoint sets A and B, A ∩ B = ϕ.


Solved examples of intersection of sets using Venn diagram:

1. If A = {1, 2, 3, 4, 5} and B = {1, 3, 9, 12}. Find A ∩ B using venn diagram.

Solution:

According to the given question we know, A = {1, 2, 3, 4, 5} and B = {1, 3, 9, 12}

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

Examples of Intersection of Sets

Therefore, from the venn diagram we get A B = {1, 3}


2. From the adjoining figure find A intersection B.

Intersection using Venn Diagram

Solution:

According to the adjoining figure we get;

Set A = {m, p, q, r, s, t, u, v}

Set B = {m, n, o, p, q, i, j, k, g}

Therefore, A intersection B is the set of elements which belong to both set A and set B.

Thus, A ∩ B = {p, q, m}

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 Intersection of Sets using Venn Diagram 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. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More