1. Introduction A set is a collection of objects.
The objects in a set are called elements of the set.

2. Notation When talking about a set we usually denote
the set with a capital letter.
Roster notation is the method of describing
a set by listing each element of the set.
Example: Let set A = The set of odd numbers
greater than zero, and less than 10. The roster
notation of A={1, 3, 5, 7, 9}

3. More on Notation Sometimes we can’t list all the
elements of a set. For instance,
Z = The set of integer numbers.
We can’t write out all the integers, there infinitely many integers. So we adopt a convention using dots …
The dots mean continue on in
this pattern forever and ever.
Z = { …-3, -2, -1, 0, 1, 2, 3, …}
W = {0, 1, 2, 3, …} = This is the set
of whole numbers.

4. Set – Builder Notation When it is not convenient to list all
the elements of a set, we use a notation the employs the rules in which an element is a member of the set. This is called set – builder notation.
A = {x | x > 5} = This is the set A
that has all real numbers greater than 5.
The symbol | is read as such that.

5. Universal Set and Subsets
The Universal Set denoted by U or Ω
is the set of all possible elements used in a problem.
When every element of one set is
also an element of another set, we say the first set is a subset.
Example A={1, 2, 3, 4, 5} and B={2, 3}
We say that B is a subset of A. The notation we use is B A.

6. The Empty Set The empty set is a special set.
It contains no elements. It is usually denoted as { } or

7. Intersection of sets
When an element of a set belongs to two or more sets we say the sets will intersect.
The intersection of a set A and a set B
is denoted by A ∩ B.
A ∩ B = {x| x is in A and x is in B}
Example A={1, 3, 5, 7, 9} and
B={1, 2, 3, 4, 5}
Then A ∩ B = {1, 3, 5}. Note that
1, 3, 5 are in both A and B.
Venn Diagram- overlapping part

8. Union of sets The union of two sets A, B is denoted by A U B.
A U B = {x| x is in A or x is in B}
Using the set A and the set B from
the previous slide, then the union of A, B is
A U B = {1, 2, 3, 4, 5, 7, 9}.
The elements of the union are in
A or in B or in both. If elements are in
both sets, we do not repeat them.
Venn Diagram: all elements from both sets

9. Complement of a Set The complement of set A is denoted by A’ or by AC.
A’ = {x| x is not in set A}.
Example Say U={1,2,3,4,5}, A={1,2}, then A’ = {3,4,5}.