Question

Given an example of the set which can be written in the set builder form but cannot be written in the roster form.

Answer 1

We can write a finite set in Roster form easily. But when there are infinite number of elements, it is difficult to write all of them in the Roster form.
For example, the set of Integers, Natural Numbers, or Rational Numbers can be described easily in set builder form but not in a Roster form.

Consider the set of rational numbers 'Q'. In the set builder form it is written as, $Q=\{\frac{a}{b}|a\in I,b\in Iandb\ne 0\}$. But Q cannot be written in roster form.