Results 1 to 3 of 3

Math Help - Equivalence Relation Proof

  1. #1
    Newbie
    Joined
    May 2013
    From
    Everywhere
    Posts
    1

    Equivalence Relation Proof

    So, here is the question:

    "Suppose ~ is a relation on A that is reflexive and has the property that for all elements a, b, and c in A, if a~b and a~c, then b~c. Prove that ~ is an equivalence relation on A."

    This is from Keef and Guichard's "An Introduction to Higher Mathematics," through which I am trying to slog right now (see link for PDF: http://people.whitman.edu/~gordon/higher_math.pdf).

    On the text's p. 27 in ch. 1.7, #5 (written out above) is currently stumping the hell out of me. I know that Reflexivity is obviously given, but I don't know how to pull out Symmetry and Transitivity from the rest of the problem.

    Can someone please help me? Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,388
    Thanks
    1476
    Awards
    1

    Re: Equivalence Relation Proof

    Quote Originally Posted by dpmagee10 View Post
    "Suppose ~ is a relation on A that is reflexive and has the property that for all elements a, b, and c in A, if a~b and a~c, then b~c. Prove that ~ is an equivalence relation on A."
    Symmetry and Transitivity from the rest of the problem.

    For Symmetry
    Suppose that x\sim y. The from being reflexive we know that x\sim x

    Now we have x\sim y~\&~ x\sim x. Apply the definition of the relation,


    For Transitivity.
    Suppose that s\sim t~\&~t\sim u.

    From that, how and why do we know that t\sim s~?~ Again apply the definition of the relation.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,417
    Thanks
    718

    Re: Equivalence Relation Proof

    Quote Originally Posted by dpmagee10 View Post
    "Suppose ~ is a relation on A that is reflexive and has the property that for all elements a, b, and c in A, if a~b and a~c, then b~c. Prove that ~ is an equivalence relation on A."
    Relations satisfying the property above are sometimes called Euclidean.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. equivalence relation proof
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 3rd 2011, 05:18 AM
  2. Equivalence relation proof
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: May 17th 2011, 04:30 PM
  3. Equivalence Relation Proof
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: March 25th 2011, 08:32 AM
  4. Equivalence Relation Proof
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: August 5th 2009, 12:19 PM
  5. equivalence relation proof
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: July 3rd 2006, 01:46 PM

Search Tags


/mathhelpforum @mathhelpforum