o
o
The dots at the end tell us that the list of odd numbers continue indefinitely . E . g .: The set of odd natural numbers is represented by { 1 , 3 , 5 , …}.
In roster form , an element is not generally repeated , i . e ., all the elements are taken as distinct .
E . g . The set of letters forming the word ‘ SCHOOL ’ is { S , C , H , O , L } .
Set Builder Form
In set-builder form , all the elements of a set possess a single common property which is not possessed by any element outside the set .
o In the set { a , e , i , o , u }, all the elements 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 = { x : x is a vowel in English alphabet }. o
Please note that any other symbol like the letters y , z , etc . could be used .
o The symbol should be followed by a colon “ : ”. o
o
After the sign of colon , we write the characteristic property possessed by the elements of the set and then enclose the whole description within braces .
If a set of number doesn ’ t follow any pattern , it can ’ t be written in set builder form .
More Example of set builder form o
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 .
Numerical : Write the set { x : x is a positive integer and x < 4 } in the roster form .
Solution : Since the set has natural numbers less that 4 , Set A ={ 1,2,3 }