Question

Write the set G = {1, 4, 9, 16, 25 …., 10} in the set builder form.

Answer 1

Hint: Find the common quality of elements of the set (that is try to find out a common form in which the entire elements of the set can be expressed).

Complete step-by-step answer:

 Observe that these numbers are the square of some numbers. They are as follows,
$
  1 = {1^2} \\
  4 = {2^2} \\
  9 = {3^2} \\
  16 = {4^2} \\
  25 = {5^2} \\
   \vdots \\
  100 = {10^2} \\
$
Since, we have got the common quality so we can represent each element of the given set G as x. which is $G = \{ x:x = {n^2},{\text{ where n is natural number from 1 to 10}}\} $ and it’s nothing but the set builder form of the given set.

Note: Set builder form is nothing but finding the common quality in elements of the set. Common quality is the benchmark on which the set is built. Perhaps, that is why this form of representation of set is called set builder form of representation of sets.