**Commutative property of set worksheet :**

Here we are going to see some practice questions on commutative property.

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

(i) Set union is commutative

(A U B) = (B U A)

(ii) Set intersection is commutative

(A n B) = (B n A)

(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.

(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.

**Question 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 :**

**Question 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)**

- Venn diagram A U B
- Venn diagram A n B
- Venn diagram of A'
- Venn diagram of B'
- Venn diagram of (AUB)'
- Venn diagram of (AnB)'
- Venn diagram of A\B
- Venn diagram of B\A

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