Results 1 to 5 of 5

Math Help - help on relation

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    8

    help on relation

    could anyone help with any part of this i think part 3 and 5 are symmetric im not sure about the rest
    Attached Thumbnails Attached Thumbnails help on relation-algebra.bmp  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    The image contains the following text:

    Which of the following relations R on sets X are reflexive, symmetric, transitive? Give proofs or counterexamples.

    1. X\, =\, \mathbb{N},\, (a,b)\,\in\, R if and only if a divides b
    2. X\, =\, \mathbb{R},\, (a,b)\, \in\, R if and only if a\, \leq \,b
    3. X\, =\, \mathbb{C},\, (a,b)\, \in\, R if and only if \left|a\right|\, =\, \left|b\right|
    4. X\, =\, \mathbb{Z},\, (a,b)\, \in \, R if and only if a\, -\, b is a multiple of 5
    5. X is the set of countries in Europe, (a,b)\, \in \, R if and only if a and b have a common border.
    Last edited by stapel; February 3rd 2009 at 10:48 AM. Reason: Wasn't done typesetting yet; must learn to click more carefully!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2009
    Posts
    32
    i think part 3 and 5 are symmetric im not sure about the rest
    Symmetry can be easily checked by swapping a and b:

    i. Not symmetric. For instance, 1 divides 5, but 5 doesn't divide 1.
    ii. Not symmetric. For instance 1 \leq 5 is true, but  5 \leq 1 is false.
    iii. Symmetric. If \left|a\right|\, =\, \left|b\right|, then \left|b\right|\, =\, \left|a\right|
    iv. Symmetric. If a - b = 5A, A is an integer, then b - a = -5A. In both cases, 5A and -5A are multiples of five.
    v. Symmetric. If a shares a border with b, then b shares a border with
    a.

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jan 2009
    Posts
    8
    any idea which of the others are relexive or transitive?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,912
    Thanks
    1760
    Awards
    1
    Well, iii is an equivalence relation so it is all three: reflexive, symmetric and transitive.
    For v, does any county share a border with itself? If so then that relation is reflexive.
    Do that for each of the other relations: is it true that each term is related to itself?
    Is this true: a \le b\;\&\; b\le c means that a \le c? If so, then the relation is transitive.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 7th 2011, 12:46 AM
  2. Relation
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: April 13th 2010, 08:13 PM
  3. Replies: 1
    Last Post: March 1st 2010, 08:24 AM
  4. Relation ( Equivalence Relation)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: December 5th 2008, 09:55 AM
  5. relation ~
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: May 21st 2005, 01:58 AM

Search Tags


/mathhelpforum @mathhelpforum