Results 1 to 4 of 4

Math Help - Relation that is 1-1, reflexive, but not symmetric

  1. #1
    Member
    Joined
    Sep 2010
    Posts
    151
    Thanks
    1

    Relation that is 1-1, reflexive, but not symmetric

    Lets say a set A has seven elements . Can a relation on A be 1-1, reflexive, but not symmetric?

    I say no its impossible cause in order to be not symmetric and reflexive we would have to use an element in the domain more than once and that would not make it 1-1.

    What do you think?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    44

    Re: Relation that is 1-1, reflexive, but not symmetric

    If R\subset A\times A is reflexive, then (a,a)\in R for all a\in A . If R is one to one, then (a,b)\in R and (a,c)\in R implies b=c that is, necessarily R=\Delta=\{(a,a):a\in A\} . This means that R is the equality relation on A (equivalence relation).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2010
    Posts
    151
    Thanks
    1

    Re: Relation that is 1-1, reflexive, but not symmetric

    So no?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    44

    Re: Relation that is 1-1, reflexive, but not symmetric

    Quote Originally Posted by Aquameatwad View Post
    So no?
    Yes, no.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Transitive, Symmetric, Non-Reflexive Relation
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: April 24th 2010, 07:12 AM
  2. Symmetric, transitive, not reflexive?
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 2nd 2010, 12:32 AM
  3. Relation, reflexive, symmetric and trasitive
    Posted in the Discrete Math Forum
    Replies: 10
    Last Post: September 27th 2009, 11:19 AM
  4. Reflexive, Transitive, Symmetric
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: May 20th 2009, 02:24 PM
  5. Reflexive and symmetric
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: March 12th 2009, 04:56 AM

Search Tags


/mathhelpforum @mathhelpforum