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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}}

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