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



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


Answer: (2)

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



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}

We read it as,

"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}



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