Set Builder Notation

In roster form, the order in which the elements are listed is immaterial. It may be noted that while writing the set in roster form an element is not generally repeated, i.e., all the elements are taken as distinct. For example, the set of letters forming the word ‘SCHOOL’ is { S, C, H, O, L} or {H, O, L, C, S}. Here, the order of listing elements has no relevance.

In set-builder form, all the elements of a set possess a single common property which is not possessed by any element outside the set.  For example, in the set {a, e, i, o, u}, all the elements possess a common property, namely, each of them is a vowel in the English alphabet, and no other letter possesses this property. Denoting this set by V, we write V = {x: x is a vowel in English alphabet}