**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.

**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)**

- 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

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.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**