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 $\overline{B}$.

3.
Understanding How to Use Set Notation
Consider the following information:
 Universal set $U$ = {$0, 1, 2, 3, 4, 5, ...$}
 Set $N$ = {all natural numbers}
 Set $A$ = {$0$}
 Set $B$ = { }

4.
Consider the following Venn Diagram:
 Universal set $U =$ {archery, eating, chess, darts, soccer, basketball, football, volleyball, badminton}
 Set $A =$ {archery, eating, chess, darts}
 Set $B =$ {soccer, basketball, football, volleyball}

5.
Consider the following Venn Diagram:

6.
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}