**Union of sets :**

Union is one of the important operations on sets which can be used to combine two or more sets to form another set.

Let us discuss this operation in detail.

Let X and Y be two sets.

Now, we can define the following new set.

**X u Y = {z | z ∈ X or z ∈ Y}**

(That is, z may be in X or in Y or in both X and Y)

X u Y is read as "X union Y"

Now that X u Y contains all the elements of X and all the elements of Y and the figure given below illustrates this.

It is clear that X ⊆ X u Y and also Y ⊆ X u Y

Example :

Let A = { 1, 3, 5, 6 }, B = { 0, 5, 6, 7 }, find A u B.

Solution :

A u B = { 1, 3, 5, 6 } u { 0, 5, 6, 7 }

A u B = { 0, 1, 3, 5, 6, 7 }

Apart from the operation union on sets, we have some other important operations on sets.

When two or more sets are combined together to form another set under some given conditions, then these operations on sets are carried out.

**Let us discuss the other important operations here:**

The other important operations on sets are.

1. Intersection

2. Set difference

3. Symmetric difference

4. Complement

5. Disjoint sets

Let us discuss the above operations in detail one by one.

Let X and Y be two sets.

Now, we can define the following new set.

**X n Y = {z | z ∈ X and z ∈ Y}**

(That is z must be in both X and Y)

X n Y is read as "X intersection Y"

Now that X n Y contains only those elements which belong to both X and Y and the figure given below illustrates this.

It is trivial that that X n Y ⊆ X and also X n Y ⊆ Y

Let X and Y be two sets.

Now, we can define the following new set.

**X \ Y = {z | z ∈ X but z ∉ Y}**

(That is z must be in X and must not be in Y)

X \ Y is read as "X difference Y"

Now that X \ Y contains only elements of X which are not in Y and the figure given below illustrates this.

Some authors use A - B for A \ B. We shall use the notation A \ B which is widely used in mathematics for set difference.

Let X and Y be two sets.

Now, we can define the following new set.

**X Δ Y = (X \ Y) u (Y \ X)**

X Δ Y is read as "X symmetric difference Y"

Now that X Δ Y contains all elements in X u Y which are not in X n Y and the figure given below illustrates this. .

If X ⊆ U, where U is a universal set, then U \ X is called the compliment of X with respect to U. If underlying universal set is fixed, then we denote U \ X by X' and it is called compliment of X.

**X' = U \ X **

The difference set set A \ B can also be viewed as the compliment of B with respect to A.

Two sets X and Y are said to be disjoint if they do not have any common element. That is, X and Y are disjoint if

** X n Y =** ᵩ

It is clear that n(A u B) = n(A) + n(B), if A and B are disjoint finite set.

After having gone through the stuff given above, we hope that the students would have understood "Union of sets".

Apart from the stuff given above, if you want to know more about "Union of sets", please click here

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**