# 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. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

You can also visit the following web pages on different stuff in math.

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