15.1 Venn Diagrams.

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Presentation transcript:

15.1 Venn Diagrams

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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.

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.

All the elements NOT in A!

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

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

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 100. How many are: both prime and a factor of 100? a factor of 100 but not prime?