Solution The required numbers are 1 2 3 4 5 6 So the given set in the roster form is 1 2 3 4 5 6 Example 3 Write the set A 1 4 9 16 25 in set builder form Solution We may write the set A as A x x is the square of a natural number Alternatively we can write A x x n where n N Example 4 Write the set 1 2 3 4 5 6 2 3 4 5 6 7 in the set builder form Solution We see that each member in the given set has the numerator one less than the denominator Also the numerator begin from 1 and do not exceed 6 Hence in the set builder form the given set is n Isns6 where n is a natural number and 1 n 6 n 1 ed Example 5 Match each of the set on the left described in the roster form with the same set on the right described in the set builder form 1 P R I N C A L a x x is a positive integer and is a divisor of 18 b x x is an integer and x 9 0 ii 0 ii 1 2 3 6 9 18 c x x is an integer and x 1 1 iv 3 3 d xx is a letter of the word PRINCIPAL Solution Since in d there are 9 letters in the word PRINCIPAL and two letters P and I are repeated so i matches d Similarly ii matches c as x 1 1 implies x 0 Also 1 2 3 6 9 18 are all divisors of 18 and so iii matches a Finally x 9 0 implies x 3 3 and so iv matches b EXERCISE 1 1 1 Which of the following are sets Justify your answer i The collection of all the months of a year beginning with the letter J ii The collection of ten most talented writers of India in A team of eleven best cricket batsmen of the world iv The collection of all boys in your class v The collection of all natural numbers less than 100 vi A collection of novels written by the writer Munshi Prem Chand vii The collection of all even integers