Results 1 to 2 of 2

Math Help - Set Theory

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    15

    Set Theory

    Cn
    Last edited by chillerbros17; February 28th 2007 at 03:22 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by chillerbros17 View Post
    Consider sets A and B with |A| = r and |B| = s with r>s>0. Explain.

    (a) What is the minimum value of |A U B|?
    The minimum value is when all the elements repeat.
    That is, B is contained fully in A.
    Thus, A U B = A.
    Thus, |A U B|=|A|=r.
    (b) What is the maximum value of |A U B|?
    When all elements are distincy, that is A and B are disjoint.
    Then |A U B| = |A|+|B| - |A (intersect) B| =|A|+|B| *


    *)By inclusion-exclusion.
    (c) What is the minimum value of |A intersect B|?
    When A and B are disjoint.
    That is A intersect B = empty.
    Thus, |A intersect B| = 0.

    (d) What is the maximum value of |A intersect B|?
    When B is fully contained in A.
    Then, A intersect B = B
    Thus,
    |A intersect B|=s.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Textbooks on Galois Theory and Algebraic Number Theory
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 8th 2011, 07:09 PM
  2. Set Theory Help
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: May 3rd 2011, 03:49 PM
  3. Group Theory - Sylow Theory and simple groups
    Posted in the Advanced Algebra Forum
    Replies: 16
    Last Post: May 16th 2009, 12:10 PM
  4. Problems relating Theory of Automata (Computer Theory)
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: October 17th 2007, 10:52 AM
  5. Set theORY
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 25th 2007, 08:01 PM

Search Tags


/mathhelpforum @mathhelpforum