subset, superset, powerset, intervals of sets

Union, Intersection, complement, difference and venn diagram of sets

Cartesian product of sets and Cartesian product arrow diagrrams

# Sets

Sets is a collection of distinct, distinguishable and well defined objects. all objects of sets are distinct (no object is repeated). object belongs to a set is known as elements of set or member of set.

**Representation of sets : ** Sets reresented between { } braces and elements of sets separated by commaas.

For Example

1) if any set is a collection of all odd number lying between 1 and 10 then we write set as A={3, 5, 7, 9}

2) if any set is collection of all vowels then we write set as B=(a, e, i, o, u)

3) if set is collection of all natural number then we write set as N={1, 2, 3, 4,....}

4) if set is collection of family member Abhay, Amit and Ashis then we write set as F={Abhay, Amit, Ashis}

## Type of Sets

- Finite sets
- Infinite Sets
- Equal sets
- Null, Empty, void sets
- Singleton sets
- Pair Sets
- Set of sets

**Finite sets :**Any set having finite number of element then that set is known as finite set.

Example: A={1, 2, 3, 4}

B={1, 3, 5}

**Infinite Sets :**If any set having infinite number of element then that set is known as infinite set.

Example: A={1, 2, 3, 4, 5, .....}

B={1, 3, 5, 7, .....}

**Equal sets :** Two sets A and B are said to be equal if each element of A is an element of set B and each element of set B is an element of set A.

**Null, Empty, void sets :** A set having no element is known as Null set, Empty set or void set. Null, Empty, void set denoted by { } (only open braces and close braces)no element between braces

**Singleton sets :** If any set having single element then that set is known as Singleton set.

**Pair Sets :** If any set having only two element then that set is known as pair set

**Set of sets :**set of sets is a set that having collection of set as a element is known as Set of sets.

Example: A={ {1,2}, {2}, {3, 4} }

B={{ram,mohan}, {abhay,prakash}, {nishant, kabir}}