Results 1 to 2 of 2

Math Help - Relations question

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    21

    Relations question

    My textbook does an erratic job of presenting relations to the reader, my professor is of no help, and I'm thoroughly puzzled, particularly with this question.

    For each of the following relations defined on the set {1,2,3,4,5}, determine whether the relation is reflexive, irreflexive, symmetric, antisymmetric, and/or transitive:

    a. R = {(1,1),(2,2),(3,3),(4,4),(5,5)}

    b. R = {(1,2),(2,3),(3,4),(4,5)}

    c. R = {(1,1),(1,2),(1,3),(1,4),(1,5)}

    d. R = {(1,1),(1,2),(2,1),(3,4),(4,3)}

    e. R = {1,2,3,4,5} x {1,2,3,4,5}

    --

    Could someone walk me through some of these so I can understand the logic? I understand the essential meaning of a relation and how to apply these terms to the classical symbolic relations, but this is puzzling to me.

    I appreciate your help.

    Regards.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2008
    From
    Paris
    Posts
    354
    Hi
    A relation \mathcal{R} can be completely determined by its graph, which here is named R, and which is a set of ordered pairs such that: (a,b)\in R\Leftrightarrow a\mathcal{R}b. (I guess that most people will say that a relation and it's graph are the same thing)

    For 1), for instance, a way to check wether R is a relation or not:

    Reflexivity: \forall a\in\{1,2,3,4,5\},\ (a,a)\in R . (i.e. aRa). That's true, thus R is reflexive.

    Irreflexivity: \forall a\in\{1,2,3,4,5\},\ (a,a)\notin R . (i.e. no(aRa) ) It's wrong, for example (1,1) is in R.

    symmetry: \forall a,b\in\{1,2,3,4,5\},\ (a,b)\in R\Rightarrow (b,a)\in R . That's the case.

    antisymmetry: \forall a,b\in\{1,2,3,4,5\},\ ((a,b)\in R\wedge a\neq b)\Rightarrow\neg((b,a)\in R) . Again, that's true (since there is no (a,b) in R with a \neqb)

    transitivity: \forall a,b,c\in\{1,2,3,4,5\},\ ((a,b)\in R\wedge (b,c)\in R)\Rightarrow (a,c)\in R . True, for the same reason given for antisymmetry.


    (That relation is particular, it's the equality)
    Last edited by clic-clac; February 16th 2009 at 11:04 PM. Reason: cor
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Relations and Functions - Inverse Relations Question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 13th 2011, 12:20 PM
  2. Replies: 1
    Last Post: September 19th 2011, 01:09 PM
  3. Relations Question
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: March 4th 2010, 09:13 AM
  4. Question About Relations?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 28th 2010, 08:55 AM
  5. Relations Question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 16th 2009, 08:01 AM

Search Tags


/mathhelpforum @mathhelpforum