( a ), ( b ) and ( c ) above in roster form by A, B, C, respectively, then A, B, C can also be represented in set-builder form as follows: A= { x : x is a natural number which divides } B= { y : y is a vowel in the English alphabet} C= { z : z is an odd natural number} Example Write the solution set of the equation x + x – = in roster form. Solution The given equation can be written as ( x – ) ( x + ) = , i. e., x = , – Therefore, the solution set of the given equation can be written in roster form as { , – }. Example Write the set { x : x is a positive integer and x < } in the roster form.
MATHEMATICS Solution The required numbers are , , , , , . So, the given set in the roster form is { , , , , , }. Example Write the set A = { , , , , , . .
. }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 Write the set { } , , , , , 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 and do not exceed . Hence, in the set-builder form the given set is where is a natural number and x : x , ≤ ≤ Example 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 :