SET THEORY

Set Theory

Set Theory

Set

A set is a well-defined collection of objects.

Subset

If every element in Set A is also in Set B, then Set A is a subset of Set B.

Proper subset

If S^' of a set S, denoted S^' subset S, is a subset that is strictly contained in S and so necessarily excludes at least one member of S. The empty set is therefore a proper subset of any nonempty set.

For example, consider a set {1,2,3,4,5}. Then {1,2,4} and {1} are proper subsets, while {1,2,6} and {1,2,3,4,5} are not.

Complement

The complement of an event is the event not occuring. Thus, ...