Set notation  Set Theory
Set notation
Lessons
Notes:
Here are some terms that we need to know for set notations:
Set: A list of objects or numbers.
Element: An object or a number in a set.
n($A$): The number of elements in set $A$.
Subset: A set where all its elements belong to another set.
Universal Set: A set of all elements in a particular context.
Empty Set: A set with no elements.
Disjoint: Two or more sets that do not have any elements in common.
Mutually Exclusive: Two or more events that cannot happen simultaneously.
Finite Set: A set with a finite number of elements.
Infinite Set: A set with an infinite number of elements.
Complement: The list of remaining elements in the universal set that is not in the mentioned set. If $B$ is a set. Then we defined the complement to be $B'$ or $\overline{B}$.
Disjoint: Two or more sets that do not have any elements in common.
Mutually Exclusive: Two or more events that cannot happen simultaneously.
Finite Set: A set with a finite number of elements.
Infinite Set: A set with an infinite number of elements.

a)
Definitions and Terms

b)
Drawing Venn Diagrams with Sets


a)
Is set $N$ a finite set or an infinite set? What about set $B$ ?

b)
List all disjoint sets, if any.

c)
Determine $n(N)$ , $n(A)$ if possible.

d)
Patsy made a statement saying that $n(A)=n(B)$ . Is this true?

e)
Is the statement $N \subset U$ true?


a)
Explain what the sets $A,B$ and $U$ represent.

b)
List all disjoint sets, if any.

c)
List all the elements of $B'$ .

d)
Show that $n(A)+n(A?)=n(C)$ .


3.
Drawing and Interpreting Venn Diagrams
Consider the following information:
 Universal Set $U =$ {10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
 Set A = {positive odd number up to 10}
 Set B = {positive even number up to 10}
 Set C = {0}