**Representation of set operations using venn diagram :**

In this section, we are going to learn, how to represent set operations using venn diagram.

**Venn diagram of union :**

**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 of intersection :**

**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 of 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 of 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 of 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.

After having gone through the stuff and examples, we hope that the students would have understood, "Representation of set operations using venn diagram"

Apart from the stuff and examples, if you want to know more about, "Representation of set operations using venn diagram", please click here.

Apart from the stuff given in this section, 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**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...