Question

what is set builder form?

Answer 1

In set-builder representation of a set, all the elements of the set have a single common property that is exclusive to the elements of the set i.e., no other element outside the set has that property.
In set-builder form, we describe an element of a set by a symbol x (though we may use any other small letter), which is followed by a colon (:). After the colon, we describe the characteristic property possessed by all the elements of that set.
For example, consider a set L as L = {6, 7, 8}
This set can be written in set-builder form as:
L = {x: x is an integer greater than 5 and less than 9}
Another way of writing the set L in set builder form as:
L = {x: (x – 6) (x – 7) (x – 8) = 0}
Thus, given set may be written in set builder forms in different ways.