Ch8.6-Inclusion-exclusion-Applications-part-1.ppt - Applications of the Principle of InclusionExclusion Part I Jorge A Cobb The University of Texas at

Ch8.6-Inclusion-exclusion-Applications-part-1.ppt -...

This preview shows page 1 - 5 out of 14 pages.

1 Applications of the Principle of Inclusion- Exclusion Part I Jorge A. Cobb The University of Texas at Dallas
Image of page 1

Subscribe to view the full document.

2 Alternative form of Inclusion-Exclusion Assume we have a universe U , | U | = N ( U ) Assume we have n object properties, P 1 , …, P n Example: Universe of cars P 1 = car is sedan P 3 = car is blue P 2 = car is minivan P 4 = car is black Let A i be the subset of U with property P i . A 1 = set of cars that are sedans Let N ( P j 1 P j 2 ... P j k ) the number of elements with properties P j 1 , P j 2 , ..., P j k , i.e., | A j 1 A j 2 ... A j k | E.g. N ( P 1 P 4 ) = number of cars that are black sedans.
Image of page 2
Continued …. Let N ( P j 1 P j 2 ... P j k ) the number of elements with properties P j 1 , P j 2 , ..., P j k , i.e., | A j 1 A j 2 ... A j k | Let P i ′ be the negation (opposite) of P i , We are interested in the number of objects without any property 3 ) ( ) 1 ( ) ( ) ( ) ( | | ) ' ' ' ( 2 1 1 1 1 2 1 2 1 n n n k j i k j i n j i j i n i i n n P P P N P P P N P P N P N N A A A N P P P N
Image of page 3

Subscribe to view the full document.

4 The number of onto functions A function f : A→B is onto or surjective iff for every y
Image of page 4
Image of page 5
  • Fall '19
  • p1, n object properties

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes