1 / 35

Use Tools of Set Algebra to Solve

Use Tools of Set Algebra to Solve. Pamela Leutwyler. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the

jvelasquez
Télécharger la présentation

Use Tools of Set Algebra to Solve

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Use Tools of Set Algebrato Solve Pamela Leutwyler

  2. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. How many men are there? How many women are doctors? How many lawyers drive Porsches?

  3. tool box To solve this problem, you might use the following: A B z x y x+y+z =x+y + y+z - y n(A B)=n(A)+n(B) -n(A B) The complement of the universe = the empty set. U  = 

  4. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches.

  5. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. If D L = U D  L  then (D L)  = U then D   L = 

  6. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. If L  W D  L  then W  L  and W  = M M

  7. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. If D  P D  L  P  then P  D  M

  8. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. 3 do not drive Porsches. D  L  P  M 3

  9. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. n(U) = n( D L) = 30 D  L  n(DL)=n(D)+n(L)-n(DL) P  M 30 = 21 + 17 - 8 3

  10. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. n(U) = n( D L) = 30 D  L  n(DL)=n(D)+n(L)-n(DL) P  M 30 = 21 + 17 - 8 3 8

  11. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. D  L  P  M 3 6 8

  12. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. D  L  P  M 3 6 4 8

  13. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. D  L  P  M 3 9 6 4 8

  14. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. D  L  P  M 3 9 6 4 8

  15. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. How many men are there? How many women are doctors? How many lawyers drive Porsches? D  L  P  M 3 9 6 4 8

  16. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. How many men are there? 9 How many women are doctors? How many lawyers drive Porsches? D  L  P  M 3 9 6 4 8

  17. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. How many men are there? 9 How many women are doctors? 12 How many lawyers drive Porsches? D  L  P  M 3 9 4 6 8

  18. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. How many men are there? 9 How many women are doctors? 12 How many lawyers drive Porsches? 14 D  L  P  M 3 9 6 4 8

  19. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. How many men are there? 9 How many women are doctors? 12 How many lawyers drive Porsches? 14 D  L  P  M 3 9 6 4 8

  20. a different approach

  21. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches.

  22. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. D L

  23. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. W D L

  24. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. W P D L

  25. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. W P 0 D L 0 0 0 0

  26. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. W P 0 D L 0 0 0 0

  27. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. n(U) = n( D L) = 30 W P 0 n(DL)=n(D)+n(L)-n(DL) D L 30 = 21 + 17 - 8 0 8 0 0 0

  28. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. W P 0 D L 0 8 0 0 0

  29. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. 3 do not drive Porsches W P 0 D L 3 0 8 0 0 0

  30. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. W P 0 D L 3 6 0 8 0 0 0

  31. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. W P 0 D L 3 6 0 8 4 0 0 0

  32. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. W P 0 D L 3 6 0 8 4 9 0 0 0

  33. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. How many men are there? 9 How many women are doctors? 12 How many lawyers drive Porsches? 14 W P 0 D L 3 6 0 8 4 9 0 0 0

  34. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. How many men are there? 9 How many women are doctors? 12 How many lawyers drive Porsches? 14 W P 0 D L 3 6 0 8 4 9 0 0 0

  35. 30 friends meet at a college reunion. They are all trying to impress one another. Every one of them has a medical degree or a law degree and some have both. All the lawyers are women. All the doctors drive Porsches. There are 17 lawyers. There are 21 doctors. 27 drive Porsches. 18 women drive Porsches. How many men are there? 9 How many women are doctors? 12 How many lawyers drive Porsches? 14 W P 0 D L 3 6 0 8 4 9 0 0 0

More Related