**Set**is an important part of mathematics.

**Set in mathematics**can be defined like this. "In real life well-defined collections, lists, or classes is called, Set."

## Set in mathematics

Collections may be pens, animals, humans, rivers, countries anything like this. In a

**set,**each of the collections is called an element or member of that set.Name of a set, Elements of a set

A

**set**is named with capital letters like A, B, C, D, etc.**Set**elements are small letters a, b, c, d, etc or numbers.Let 23, 34, 24, 42 are elements of a set, and the name of that set is A. We have to write like this-

A= {23, 34, 24, 42}

Elements are written into the second bracket and separated with commas. This representation process is called tabular form.

Again,

Let in a set B elements are all the countries of South Asia. Here we can write,

B = {x: x is a country and situated in South Asia}

": " sign is called such that. This set representation style is called set building form. " | " sign is used also in some cases.

- If a is an element of set A then a∈A is written. The sign ∈ is called belongs to.

- If a is an element of set A then we can say a belongs to A.
- If b is not an element of set A then b∈A is written. It is called b is not belongs to A.

A= {23, 34, 24, 42}

Here. 23∈A but 13∉A

### Some types of sets

#### Empty set

If any set contains no element then the set is called an empty set. An empty

**Set in mathematics**is defined by the ∅ sign.∅ = { x : x² = 4 and x odd}

It is an empty set because by squaring any odd number we will not get x² = 4.

Remember: Empty set is not meaning {0}. This is meaning that this set has an element that is 0.

#### Disjoint set

If there is no common element between two sets then those two sets are called disjoint sets.

#### Example:

Let two sets are A= {1, 2, 3} and B = {4, 5, 6}. Between these two sets, there are no common elements. That is why these two sets can be called disjoint sets.

#### Subset

If all the elements of a set are also members of another set then the first set is called the subset of the second set.

**Example:**

Let two sets are A= {1, 2, 3, 4, 5} and B= {2, 4, 5}.

Here you can see that all the elements of set B are also the elements of set A. In this case set B is called the subset of set A. It is written as B⊂A.

If a set A is given then a lot of subsets can be made by taking one or more elements from that set.

Let a set is X = {1, 2, 3, 4, 5, 6, 7}

Some subsets from set X are {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 2, 3} etc.

With respect to the definition of subset set X is also a subset of set X. This type of subset is called an improper subset. Except for set X, all other subsets of set X are a proper subset.

Remember: An empty set is a subset of any set.

### Finite set and Infinite set in mathematics

#### Finite set

If the limit of elements is defined for a set then the set is called a finite set.

Example: P = {5, 6, 8, 9}

{x : x is a vowel of letter}

#### Infinite set

Finite set: If the limit of elements is undefined for a set then the set is called a finite set.

Example: {2, 4, 6, 8, 10, ………….}

{x : x is real number}

So this was an overall discussion on Set in mathematics. Next, we have discussed some rules of the sets in mathematics.

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