What is Set?

A set is a well defined collection of objects.

Examples :
- Player in Indian cricket team
- Player in Australian cricket team
- Name of States in India

What is a collection

A collection of good players of India is a collection and not a set.

This is majorly because it is not well defined.

We can say that,
Every set is a collection but every collection is not a set.

Methods to represent a Set

There are two methods to represent a set.
1. Roster Form
2. Set Builder Form

Roster Form In roster form, we write all the elements.

Example : Vowels in English Language
Roster Form = {a,e,i,o,u}

Example : Natural numbers less than 9
Roster Form = {1,2,3,4,5,6,7,8}

Set Builder Form In set builder form, we write the property of the elements.

Example : Vowels in English Language
Roster Form = {\(x:x\) is a vowel in English language}

Example : Natural numbers less than 9
Roster Form = {\(x: x<10, x \in N\)}

Some Important Sets

N : the set of all natural numbers
Z : the set of all integers
Q : the set of all rational numbers
R : the set of real numbers
\(Z^+\): the set of positive integers
\(Q^+\): the set of positive rational numbers, and
\(R^+\): the set of positive real numbers.

Empty Set

A set which does not contain any element is called the empty set or the void set or null set and is denoted by { } or φ.

Finite Set

A set which contains finite nmber of elements are called finite set.

Infinite Set

A set which contains infinite nmber of elements are called finite set.

Subsets

A set A is said to be a subset of set B if every element of A is also an element of B.

In symbols we write A ⊂ B which is read as A is a subset of B

If a ∈ A it implies a ∈ B.

Example :
N ⊂ Z ⊂ Q ⊂ R,
T ⊂ R,
Q ⊄ T,
N ⊄ T

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