Results 1 to 3 of 3

Math Help - Define a relation R which is neither symmetric nor antisymmetric

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    1

    Define a relation R which is neither symmetric nor antisymmetric

    How many players must be at least a set A so that it can define a relation R which is neither symmetric nor antisymmetric. Answer detailed explanation.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,545
    Thanks
    780
    Do they refer to constituent of sets as "players" instead of "elements" now?

    Try various relations on sets with 0, 1, 2, and 3 elements. Consider, for example, antisymmetry: for all x and y, if R(x,y) and R(y,x), then x = y. Note that if it is not the case that R(x,y) and R(y,x) for some x, y, this fact does not violate antisymmetry because an implication is vacuously true when the assumption is false. So, to break antisymmetry, you need to have x and y such that the assumption is true but the conclusion is false.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,801
    Thanks
    1691
    Awards
    1
    Consider the set \{a,b,c\} and the relation \math{K}=\{(a,b),(b,c),(b,a)\}.

    Is true that \math{K} is neither antisymmetric or symmetric?

    Can you improve on the number three?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. reflexive, symmetric, antisymmetric, transitive?
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: April 8th 2011, 05:47 AM
  2. Symmetric relation v.s. symmetric matrix
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 14th 2010, 11:37 PM
  3. Replies: 2
    Last Post: January 24th 2010, 07:06 PM
  4. Replies: 1
    Last Post: April 22nd 2009, 10:59 AM
  5. define a relation...
    Posted in the Discrete Math Forum
    Replies: 12
    Last Post: December 3rd 2008, 11:21 AM

Search Tags


/mathhelpforum @mathhelpforum