REPRESENTATION OF A SET

There are two types of representation:

  1. Tabular form
  2. Set – builder form

 Tabular or roster form: A set is described by listing elements, separated by commas, in { } brackets.

Example:

  1. The set of five prime numbers can be described as {2, 3, 5, 7, 11}
  2. The set of all months having 31 days described as {January, March, May, July, August, October, December}

Set – builder form: A set is described by property of all the elements within brackets.

Example:

A = {x : x is a natural number and less than 5}

B = { x : x is a vowel of English Alphabet}

 

Roster form

Set – builder form

(1) A = \left\{ {1,2,3,4,5,6} \right\} A = \left\{ {x:x\,is\,a\,natural\,number\,less\,than\,7} \right\}
(2) B = \left\{ {0,3,6,9,.......} \right\} B = \left\{ {x:x\,is\,multiple\,of\,3} \right\}
(3) C = \left\{ {m,a,t,h,e,i,c,s} \right\} C = \left\{ {x:\,x\,is\,a\,letter\,in\,the\,word\,MATHEMATICS} \right\}
(4) D = \left\{ { - 3, - 2, - 1,0,1,2,3} \right\} D = \left\{ {x:{x^2} \le \,10,\,x \in \,Z} \right\}
(5) E = \left\{ {\frac{1}{2},\frac{1}{3},\frac{1}{4},\,\frac{1}{5},\,\frac{1}{6}} \right\} E = \left\{ {x:x\, = \frac{1}{n},\,n \in \,N,\,n > 1} \right\}
(6) F = \left\{ { - 2,2} \right\} F = \left\{ {x:{x^2} - 4 = 0} \right\}

Post Author: E-Maths