## DISTRIBUTIVE PROPERTY OF SET WORKSHEET

Distributive property of set worksheet :

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

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

(i)  Union distributes over intersection

A U (B n C) = (A U B) n (A U C)

(ii)  Intersection distributes over union

A n (B u C) = (A n B) U (A n C)

## Distributive property of set worksheet - Practice questions

(1)  Let A = {0, 1, 2, 3, 4}, B = {1, - 2, 3, 4, 5, 6} and C = {2, 4, 6, 7}.

(i) Show that A U (B n C) = (A U B) n (A U C) (ii) Verify using Venn diagram.

(2)  For A = {x : - 3  x < 4, x  R}, B = {x ; x < 5, x ∊ N} and C = {- 5, - 3, - 1,0,1,3}, Show that A n (B U C) = (A n B) U (A n C)

## Distributive property of set worksheet - Solution

Question 1 :

Let A = {0, 1, 2, 3, 4}, B = {1, - 2, 3, 4, 5, 6} and C = {2, 4, 6, 7}.

(i) Show that A U (B n C) = (A U B) n (A U C) (ii) Verify using Venn diagram.

Solution :

(B n C) = {1, - 2, 3, 4, 5, 6} n {2, 4, 6, 7}.

=  {4, 6}

A U (B n C)  =  {0, 1, 2, 3, 4} U {4, 6}

=  {0, 1, 2, 3, 4, 6} --------(1)

(A U B)  =  {0, 1, 2, 3, 4} U {1, - 2, 3, 4, 5, 6}

=  {-2, 0, 1, 2, 3, 4, 5, 6}

(A U C)  =   {0, 1, 2, 3, 4} U {2, 4, 6, 7}

=  {0, 1, 2, 3, 4, 6, 7}

(AUB) n (AUC) = {-2, 0, 1, 2, 3, 4, 5, 6} n {0, 1, 2, 3, 4, 6, 7}

=  {0, 1, 2, 3, 4, 6} --------(2)

Question 2 :

For A = {x : - 3  x < 4, x  R}, B = {x ; x < 5, x ∊ N} and C = {- 5, - 3, - 1,0,1,3}, Show that A n (B U C) = (A n B) U (A n C)

Solution :

A = {x : - 3  x < 4, x  R} that is, A consists of all real numbers from – 3 upto 4 but 4 is not included.

A = {-3, -2, -1, 0, 1, 2, 3}

B = {x ; x < 5, x ∊ N} = {1, 2, 3, 4}

(B U C)  =  {1, 2, 3, 4} U {- 5, - 3, - 1, 0, 1, 3}

=  {-5, -3, -1, 0, 1, 2, 3, 4}

An(B U C) = {-3, -2, -1, 0, 1, 2, 3} n {-5, -3, -1, 0, 1, 2, 3, 4}

=  {-3, -1, 0, 1, 2, 3}  -------(1)

(A n B)  =   {-3, -2, -1, 0, 1, 2, 3} n {1, 2, 3, 4}

=  {1, 2, 3}

(A n C)  =   {-3, -2, -1, 0, 1, 2, 3} n {- 5, - 3, - 1, 0, 1, 3}

=  {-3, -1, 0, 1, 2, 3}

(A n B) U (A n C)  =  {1, 2, 3} U {-3, -1, 0, 1, 2, 3}

=  {-3, -1, 0, 1, 2, 3}  -------(2)

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