1. 15.1
Venn Diagrams

5. mess

8. Used to separate the objects to be counted from all others.
Combinatorics
Theory of Counting
Venn Diagrams
Used to separate the objects to be counted from all others.

9. U- Universal Set (Everything in context)
U A B
U- Universal Set (Everything in context)
The circles, A and B, represent Subsets of the Universal Set.
A B is the INTERSECTION of the two subsets.
A B is the UNION of the two subsets.
Represents the Complement of A. This represents the set of all elements NOT in A.

10. All the elements NOT in A!

12. Example U – our entire class A – people who have sisters
U A B
U – our entire class
A – people who have sisters
B – people who have brothers

14. The Inclusion-Exclusion Principle
For any sets A and B,

15. Word Problems
Of the first 100 positive integers, 25 are prime, 9 are factors of 100, and 68 are neither prime nor a factor of How many are:
both prime and a factor of 100?
a factor of 100 but not prime?