Sets

A set is a well defined collection of objectives.

A = {coat, hat, scarf, gloves, boots}, where A is the name of the set, and the braces indicate that the objects written between them belong to the set.

Every object in a set is unique: The same object cannot be included in the set more than once.

Example: What is the set of all fingers?

Solution: P = {thumb, index, middle, ring, little}.

Note that there are others names for these fingers: The index finger is commonly referred to as the pointer finger; the ring finger is also known as the fourth finger, and the little finger is often referred to as the pinky. Thus, we could have listed the set of fingers as:

P = {thumb, pointer, middle, fourth, pinky}

The following conventions are used with sets:

• Capital letters are used to denote sets.

• Lowercase letters are used to denote elements of sets.

• Curly braces { } denote a list of elements in a set.

So for examples 1 through 4, we listed the sets as follows:

1. A = {coat, hat, scarf, gloves, boots}.

2. P = {thumb, index, middle, ring, little}.

3. Q = {2, 4, 6, 8}.

4. X = {red, blue, yellow}.

These sets have been listed with roster notation. Roster notation is a list of elements, separated by commas, enclosed in curly braces. The curly braces are used to indicate that the elements written between them belong to that set. Let's look at some more examples of sets listed with roster notation.