Question

Thorough explanation of sets builder Notation

Answer 1

In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by stating the properties that its members must satisfy. Forming sets in this manner is also known as set comprehension, set abstraction or as defining a set's intension. Although some simply refer to it as set notation, that label may be better reserved for the broader class of means of denoting sets.

Answer 2

this is quite thorough

http://www.mathsisfun.com/sets/set-builder-notation.html