Results 1 to 5 of 5

Math Help - Relations Help

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    3

    Relations Help

    Hi, i've been mulling over this question for a few days now and i've got an answer, but it seems too simple to be correct.

    8 = for all
    R is relation
    R is useful iff:
    (u1) (8x¬(xRx)
    (u2) 8xyz((xRy ^ yRz) implies (xRz))
    (u3) 8xyz(xRy implies (xRz OR zRy))

    Consider the relation ‘greater than’ on Natural numbers. Is it useful? Good? Cool?

    I just need a true or false for each, but they all seem to be true (there are several more examples other than these three). I think i'm going about it the wrong way, and any advice to kick me off would be much apprieciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,965
    Thanks
    1785
    Awards
    1
    The relation \mathcal{R} on \mathbb{N} by x\mathcal{R}y \text{ if and only if  } x>y.

    \left( {\forall x} \right)\left[ {x \not> x} \right].

    Clearly > is transitive. That is the second property.

    For the third property suppose \left\{ {x,y,z} \right\} \subset \mathbb{N}\;\& \; x\mathcal{R}y . This means that x>y.
    If z \geqslant x\; \Rightarrow \;z > y\; \Rightarrow \; z\mathcal{R}y
    On the other hand z < x\; \Rightarrow \;x\mathcal{R}z .
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2009
    Posts
    3
    Hi, thanks for a quick response.

    I'm understand what you have written, but i'm still not entirley clear on how to gauge if each property is true or false. This is the full part of that question:

    call a relation R useful iff it has the following properties: Then the listed properties.

    With R being >. As far as i can tell all those properties have to be true when used with the > (and the <). Maybe i'm just overthinking it and all the 5 properties in the question are true.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,965
    Thanks
    1785
    Awards
    1
    Quote Originally Posted by grandstand View Post
    Maybe i'm just overthinking it and all the 5 properties in the question are true.
    What five properties?
    You only gave three.
    Which is it?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2009
    Posts
    3
    There are 5 overall in the question.

    Let us call a relation R useful iff it has the following properties:
    (u1) 8x¬(xRx)
    (u2) 8xyz((xRy ^ yRz) implies (xRz))
    (u3) 8xyz(xRy ! (xRz OR zRy))
    We call a relation R good iff it has the following properties:
    (g1) 8x¬(xRx) (same as u1)
    (g2) 8xyvw((xRy ^ vRw) implies (xRw OR vRy))
    We call a relation R cool iff it has the following properties:
    (r1) 8x¬(xRx) (same as u1)
    (r2) 8xyvw((xRy ^ vRw) implies (xRw OR vRy)) (same as g2)
    (r3) 8xyvz((xRy ^ yRz) implies (xRv OR vRz))

    The question askes where R = > is useful, good and/or cool, but then to say which properties are true or false.
    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, 01:20 PM
  2. Replies: 1
    Last Post: September 19th 2011, 02:09 PM
  3. [SOLVED] Relations on A
    Posted in the Discrete Math Forum
    Replies: 10
    Last Post: November 21st 2010, 12:25 PM
  4. Relations in a set
    Posted in the Algebra Forum
    Replies: 3
    Last Post: September 5th 2010, 11:03 PM
  5. relations help (3)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 18th 2010, 05:49 AM

Search Tags


/mathhelpforum @mathhelpforum