#### notes

Set is a collection of well defined objects. By well defined objects, we mean the definition should not vary it should be definite.

Example 1- Collection of vowels of English alphabet. The collection will be a, e, i, o, u. This is a well defined collection.

Example 2- Collection of good maths books available in market. Here, the collection will vary form person to person because of different personal choices and preferences.

There are two methods of representing a set :

(i) Roster or tabular form

(ii) Set-builder form.

Example- Collection of vowels of English alphabet.

A= {a, e, i, o, u} this is the roster form of a set.

Here, A is represented as a set, and the elements of set are enclosed in { }.

Set builder form, A= {x: x is a vowel in English alphabet}

x represents the elements in the enclosed brackets { }.**Note:**

1) Order is immaterial. That the sequence in which the elements appear is not important, even if the sequence is changed the meaning remains same.

Take the same example- Collection of vowels of English alphabet.

A= {e, i, o, u, a}

2) Same elements are not repeated.

Example- B= set of all letters of the word SCHOOL

Roster form: B= {S, C, H, O, L}

Set-builder form: B= {x:x is letter used in word SCHOOL}

3) C= Set of all natural numbers.

Set-builder form C = {x :x ∈ N}

Roster form C= {1, 2, 3, 4, ...}

As natural numbers are infinite so we will represent them with three dots.

∈ means belongs to and ∉ means does not belongs to.

Example- A= {1, 2, 3, 4, 5, 6}

Here, 2 ∈ A, 9 ∉ A, 8 ∉ A, 5 ∈ A

We give below a few more examples of sets used particularly in mathematics, viz.

`"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.

#### description

1) Roster or Tabular method or List method

2) Set-Builder or Rule Method

3) Venn Diagram