Question

What is meant by set - builder form? Explain briefly?

Answer 1

In this method, instead of listing all elements in a set, we write the set by some special property or properties satisfied by all elements and write it as
A = {x : P(x)} = {x / x has property P(x) }

Example -
If A = { 1, 2, 3, 4 } then we can write
A = { x ∈ N : x < 5 }

Answer 2

In set - builder form, all the elements of a set possess a single common property which is not possessed by an element outside the set.

Example : Set of natural numbers k, ie,

k={x: x is a natural number}