1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Compliments Universe

  1. Apr 1, 2004 #1
    OK, if I have sets such as:

    |A| = 7
    |B| = 10
    |A intersection B| = 5
    (And the universe equaled 19)

    Then how do you find the compliment of |A intersection B|? And what would the answer be in this case? Thanks.
     
    Last edited: Apr 1, 2004
  2. jcsd
  3. Apr 1, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Do you really want to take the complement of a cardinality?
     
  4. Apr 1, 2004 #3

    ahrkron

    User Avatar
    Staff Emeritus
    Gold Member

    You may find useful to make a drawing of the situation.
     
  5. Apr 1, 2004 #4
    OK, here is the problem:

    If Universe = 19 and:
    A = People who dislike NDP
    B = People who dislike Liberals
    C = People who dislike Conservatives
    D = People who dislike Canadian Alliance
    |A| = 7
    |B| = 10
    |C| = 11
    |D| = 6
    |B intersection A| = 5
    |A intersection C| = 5
    |B intersection C| = 6
    |A intersection D| = 3
    |B intersection D| = 4
    |C intersection D| = 5
    |C intersection B intersection A| = 3
    |B intersection A intersection D| = 2
    |C intersection A intersection D| = 3
    |C intersection B intersection D| = 4
    |A intersection B intersection C intersection D| = 2

    Are all given, then how many like all 4 parties (not dislike)? Can someone point me in the right direction for this? Thank you.
     
  6. Apr 1, 2004 #5

    Zurtex

    User Avatar
    Science Advisor
    Homework Helper

    I've never done this before so this may be a really stupid comment, but wouldn't it make it just that little easier if:

    |A intersection B intersection C intersection D| = 2

    Then you can delete this line and take 2 away from all these 4 lines:

    |A| = 7
    |B| = 10
    |C| = 11
    |D| = 6

    And the universe.
     
  7. Apr 1, 2004 #6
    Not sure...

    (Not really sure where to start with this myself...)
     
  8. Apr 2, 2004 #7

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    You want [tex]A^c\cap B^c\cap C^c \cap D^C[/tex] call this set E

    Let U denote the set of all people asked (the universe)

    By definition E = (U\A)n(U\B)n(U\C)n(U\D)

    can you work with the rules of sets to simplify that?

    Or can you think of a better way of doing it? Such as: (AuB)^c = (A^c)n(B^c)?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Compliments Universe
  1. Universal Mathematicians (Replies: 12)

Loading...