What are the two methods of representing a set?

The two primary methods of representing a set are the roster method and the set-builder notation. The roster method lists all the elements of the set explicitly, using curly braces (e.g., {1, 2, 3}). In contrast, set-builder notation describes the properties that characterize the elements of the set, typically in the form {x | property of x} (e.g., {x | x is a positive integer}). Both methods effectively communicate the contents of a set but serve different purposes in mathematical contexts.