Roaster form of a set : Sets

      

                 In set theory,  there are two methods of representing a set :

 1. Roaster or Tabular form

 2. Set- Builder form

Roaster Form :

          In roaster form , all the elements of a set are listed, the elements are being                         separated by commas and are enclosed within braces { } .

 For example

 1. The set of all even positive integers lessthan 7 is described in roaster form as{ 2,4,6 }.

 2. The set of all natural numbers which divide 42 is { 1,2,3,6,7,14,21,42 }

 3. The set of all vowels in the English alphabet is { a,e,i,o,u } etc.

Note :

  In roaster form , the order in which the elements are listed is immaterial. i.e. in the        example 2, the set in the example 2 can also be written as { 1,7,2,3,14,21,42,6 } 

Set- Builder Form :

            In the set-builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set. 

 For example

 1.  In the set { a,e,i,o,u } , all the elemnts possess a common property, namely , each of          them is a vowel in the English alphabet, and no other letter possess this property. 

      Denoting this set by V, we write V as 

                                      V = { x / x is a vowel in English alphabet }

2. Suppose A = { x / x is a natural number and 3 < x < 10 } is read as " the set of all x          such that x is a natural number and x lies between 3 and 10 " . Hence, the numbers        4,5,6,7,8 and 9 are the elements of the set A. 

 * well-defined collection of objects 

 * 4th dimensional objects 

 * why | -2 | = 2 ?

 

  #intermediate #set #mathematics #iit #jee #class #classxii #class12 #cbse #roaster #form #of #set