REPRESENTATION OF SET OPERATIONS USING VENN DIAGRAM

Venn Diagram for Union of Two Sets :

A U B

Let A and B be two sets.

Now, we can define the following new set.

A U B  =  {z | z ∈ A or z ∈ B }

(That is, z may be in A or in B or in both A and B) 

A U B is read as "A union B"

To draw venn diagram for A U B, we have to shade all the regions of A and B.

Venn Diagram for Intersection of Two Sets :

A n B

Let A and B be two sets.

Now, we can define the following new set.

A n B  =  {z | z ∈ A and z ∈ B}

(That is z must be in  both A and B)

A n B is read as "A intersection B"

Now that A n B contains only those elements which belong to both A and B and the figure given above illustrates this. 

It is trivial that that A n B ⊆ A and also A n B ⊆ B

Venn Diagram for Set Difference :

To draw a venn diagram for A\B, shade the region of A by excluding the common region of A and B.

A\B

B\A 

Let A and B be two sets.

Now, we can define the following new set.

A \ B  =  {z | z ∈ A but z ∉ B}

(That is z must be in  A and must not be in B)

A \ B is read as "A difference B"

Now that A \ B contains only elements of A which are not in B and the figure given above illustrates this. 

Venn Diagram for Symmetric Difference :

To draw venn diagram for A symmetric difference B, we have to combine the venn diagram of A\B and B\A

A Δ B  =  (A\B) U (B\A)

Let A and B be two sets.

Now, we can define the following new set.

A Δ B  =  (A \ B) U (B \ A)

A Δ B is read as "A symmetric difference B"

Now that A Δ B contains all elements in A U B which are not in A n B and the figure given above illustrates this.

Venn Diagram for Complement :

To draw a venn diagram for A', we have shade the region that excludes A

A'

To draw a venn diagram for B', we have shade the region that excludes B

B'

If A ⊆ U, where U is a universal set, then U \ A is called the compliment of A with respect to U. If underlying universal set is fixed, then we denote U \ A by A' and it is called compliment of A.

A'  =  U \ A 

The difference set set A \ B can also be viewed as the compliment of B with respect to A.  

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