COMMUTATIVE PROPERTY OF SET

Commutative property of set :

Here we are going to see the commutative property used in sets.

For any two two sets, the following statements are true.

(i)  Set union is commutative

 (A U B)   =  (B U A)

(i)  Set intersection is commutative

 (A n B)   =  (B n A)

Let us look into some example problems based on above properties.

Commutative property of set - Examples

Example 1 :

For the given sets A = {- 10,0,1, 9, 2, 4, 5} and B = {- 1,- 2, 5, 6, 2,3,4}, verify that

(i) Set union is commutative. Also verify it by using Venn diagram.

(ii) Set intersection is commutative. Also verify it by using Venn diagram.

Solution :

Commutative property :

(i)  (A U B) =  (B U A)

(ii)  (A n B) = (B n A)

(i)  A = {- 10, 0, 1, 9, 2, 4, 5} and B = {- 1,- 2, 5, 6, 2, 3, 4},

A U B = {- 10, 0, 1, 9, 2, 4, 5} U  {- 1,- 2, 5, 6, 2, 3, 4} 

=  {-10, -2, -1, 0, 1, 2, 3, 4, 5, 6, 9}  ---(1)

B U A =  {- 1,- 2, 5, 6, 2, 3, 4} U {- 10, 0, 1, 9, 2, 4, 5}

=  {-10, -2, -1, 0, 1, 2, 3, 4, 5, 6, 9}  ---(2)

(1)  =  (2)

Verifying in venn diagram :

(ii)  A = {- 10, 0, 1, 9, 2, 4, 5} and B = {- 1,- 2, 5, 6, 2, 3, 4}

A n B = {- 10, 0, 1, 9, 2, 4, 5} n {- 1,- 2, 5, 6, 2, 3, 4}

=  { 2, 4, 5 } ---(1)

B n A {- 1,- 2, 5, 6, 2, 3, 4} n {- 10, 0, 1, 9, 2, 4, 5}

=  { 2, 4, 5 } ---(2)

Verifying in venn diagram :

Example 2 :

For the given sets A = {1, 2, 3,  4, 5} and B = {3, 4, 5, 6}  verify that

(i) Set union is commutative. 

(ii) Set intersection is commutative. 

Solution :

Commutative property :

(i)  (A U B) =  (B U A)

(ii)  (A n B) = (B n A)

(i)  A = {1, 2, 3,  4, 5} and B = {3, 4, 5, 6} 

A U B = {1, 2, 3, 4, 5} U  {3, 4, 5, 6} 

=  {1, 2, 3, 4, 5, 6}  ---(1)

B U A =  {3, 4, 5, 6} U {1, 2, 3,  4, 5}

=  {1, 2, 3, 4, 5, 6}  ---(2)

(1)  =  (2)

(i)  A = {1, 2, 3,  4, 5} and B = {3, 4, 5, 6} 

A n B = {1, 2, 3, 4, 5} n {3, 4, 5, 6} 

=  {3, 4, 5}  ---(1)

B n A =  {3, 4, 5, 6} U {1, 2, 3,  4, 5}

=  {3, 4, 5}  ---(2)

(1)  =  (2)

Related topics

After having gone through the stuff given above, we hope that the students would have understood "Commutative property of set". 

Apart from the stuff given above, if you want to know more about "Commutative property of set", please click here

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

Widget is loading comments...