# Identify The Sets

## Basic Concept

##### Identify The Sets

A set is a collection of well-defined objects

A set is well-defined if we are able to tell whether or not any particular object is an element of the set

Example:

Which of the following are well-defined sets?

(1)   All the tall girls of the school

(2)   All the letters in the word "mathematics"

(3)   All the hardworking teachers in a school

(4)   All the honest members in the family

All the letters in the word "mathematics" is well-defined sets

B = {m, a, t, h, e, i, c, s}

The following conventions are used with sets:

• Capital letters are used to denote sets
• Curly braces { } denote a list of elements in a set
• Lowercase letters are used to denote elements of sets

Example:

A is the set of vowels

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

The elements in the sets are depicted in either the statement form, set-builder notation form or roster form

• Statement form

A = {prime numbers between 10 and 30}

• Set-builder notation

A = {x| 10 < x < 30, x ∈ prime numbers}

"A is the set of all x such that x is more than10 but less than 30 and x belongs to prime numbers"

• Roster form

A = {11, 13, 17, 19, 23, 29}