Sets and Subsets
The lesson introduces the important topic of sets, a simple idea that recurs
throughout the study of probability and statistics.
Set Definitions

A set
is a welldefined collection of objects.

Each object in a set is called an element
of the set.

Two sets are equal
if they have exactly the same elements in them.

A set that contains no elements is called a null set or an
empty set.

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

A set is usually denoted by a capital letter, such as A, B, or C.

An element of a set is usually denoted by a small letter, such as x, y, or
z.

A set may be described by listing all of its elements enclosed in braces. For
example, if Set A consists of the numbers 2, 4, 6, and 8, we may say: A
= {2, 4, 6, 8}.

The null set is denoted by
{} or ∅.

Sets may also be described by stating a rule. We could describe Set A from
the previous example by stating: Set A consists of all the even
singledigit positive integers.
Set Operations
Suppose we have four sets  W, X, Y, and Z. Let these sets be defined as
follows: W = {2}; X = {1, 2}; Y= {2, 3, 4}; and Z = {1, 2, 3, 4}.

The union
of two sets is the set of elements that belong to one or both of the two sets.
Thus, set Z is the union of sets X and Y.

Symbolically, the union of X and Y is denoted by X
∪ Y.

The intersection
of two sets is the set of elements that are common to both sets. Thus, set W is
the intersection of sets X and Y.

Symbolically, the intersection of X and Y is denoted by X
∩ Y.