This document defines sets and set operations like union and intersection. It provides examples of sets, finding set operations, and using Venn diagrams to represent relationships between sets. Examples include defining sets, finding intersections and unions of sets, determining probabilities of sets and set combinations, and assessing independence and mutual exclusivity of events.

1. Lets talk about
Definition:
A set is a collection of objects named elements.
Notation:
A set can be defined by listing its elements between
braces. Example: A = {1, 2, 3, 4, 5}.


If something is an element of a set we use .
If something is not an element we use .
Example: , .
A
89
A
2 


2. Lets talk about
If a set has no elements it is called the empty
set. It is written as ∅.
The universal set is the set of all elements
being considered. It is written 𝜉.

3. Lets talk about
The union of two sets, A and B, is the elements
in A or B or in both. It is written A ∪ B.

The intersection of two sets, A and B, is the
elements that are in A and B. It is written A ∩ B.

4. Example 1
A = {2, 3, 5, 7, 11, 13, 17, 19}
B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
𝜉 is all the numbers 1 to 20.
a) Find A ∩ B
b) Find A ∪ B
c) What would a Venn diagram look like?

5. A B
A ∪ B
A B
A ∩ B
𝜉
𝜉

6. A B
A’
A B
A ∩ B’
𝜉
𝜉

7. Example 2
The Venn diagram shows the number of people
who like Pepsi Max and Coke Zero.
P C
a) Find P(P)
b) Find P(P ∪ C)
c) Find P(P ∩ C’)
31 5 2
9 𝜉

8. Example 3
A B
a) Find P(A) b) Find P(A’ ∩ B’)
c) Find P(A’ ∩ B)
d) Are A and B independent?
0.5 0.1 0.2
0.2 𝜉
If A and B are independent then the outcome of one
event doesn’t affect the probability of the other and
P(A) x P(B) = P(A ∩ B)

9. Example 4
P(A) = 0.25, P(B) = 0.6 and P(A ∩ B) = 0.05.
a) Draw a Venn diagram
b) Find P(A ∪ B)
c) Find P(A’ ∩ B)
d) Are A and B mutually exclusive?
If A and B are mutually exclusive then the events
cannot happen at the same time.
P(A ∩ B) = 0