This work played an important role in the development of topology, and all the basics of the subject are cast in the language of set theory. However sets are not just a tool; like many other mathematical …

De nition of the Universal Set The universal set U refers to the set that contains all other objects of interest, such that any other set A is a proper subset of U.

Method 1: Roster Notation: A roster is a list of the elements in a set, separated by commas and surrounded by French curly braces.

The set of all humans that weigh at least eight tons, for example, is the empty set. Sets whose definition contains a contradiction or impossibility are often empty.

The complement of a set A, denoted by Ac (or sometimes by A), consists of all elements that are in the universal set U but not in A, i.e., Ac = fa j a 2 U; a 62Ag.

Empty set (Null set): set that contains no elements o Example: Ø = { } Fall 2017

To prove set equality, show inclusion in both directions Let A; B; C U. Prove that (A B) C if and only if (A C) B. By the end of this lesson, you will be able to: Remember fundamental laws/rules of set theory. …