Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By emakarov

Math Help - Equivalence relationships and binary relations

  1. #1
    Newbie
    Joined
    May 2012
    From
    Aus
    Posts
    2

    Equivalence relationships and binary relations

    Let p be a binary relation defined on the integers Z by:

    apb if and only if a2 =logically equivalent to= b2(mod7)

    Prove carefully that p is an equivalence relation on Z and give the equiv classes.
    __________________________________________________ ____________________
    Let X = {p, q}
    write down the set X x X
    list all the binary relations on X which are reflexive
    A binary relation p on a set X is said to be irrelfexive if (x, x) not-element p for all x element X
    Write down all binary relations on the set X above which are irreflexive, and also irreflexive and symmetric simultaneously

    Ok, So i started with the first part and proved it by
    Took each number and squared it. The ones with the same square mod 7 are in the same equivalence class.

    0^1 ≡ 0(mod7)
    1^2 ≡ 1(mod7), 6
    2^2 ≡4(mod7), 5
    3^2 ≡2(mod7), 4

    Therefore equivalence classes are {0}, {1,6} , {2,5} and {3,5} I think?(clarification would do wonders here)

    However I am stuck from the X = {p, q} bit... and everything that follows any help would be much appreciated...

    Thanks Simmy
    Last edited by simmy; May 23rd 2012 at 06:08 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,559
    Thanks
    785

    Re: Equivalence relationships and binary relations

    Quote Originally Posted by simmy View Post
    apb if and only if a2 =logically equivalent to= b2(mod7)
    Logical equivalence refers to propositions, not numbers. Here a2 and b2 are said to be congruent modulo 7.

    Quote Originally Posted by simmy View Post
    Therefore equivalence classes are {0}, {1,6} , {2,5} and {3,5}
    The last class should be {3, 4}. In fact, since the relation is on \mathbb{Z} and not \mathbb{Z}_7, equivalence classes should be infinite. Also, you have not shown that p is an equivalence relation.

    Quote Originally Posted by simmy View Post
    Let X = {p, q}
    write down the set X x X
    X x X = {(p, p), (p, q), (q, p), (q, q)}.

    Quote Originally Posted by simmy View Post
    list all the binary relations on X which are reflexive
    A relation on X is a subset of X x X. A reflexive relation must contain (p, p) and (q, q), but it may or may not contain other pairs.
    Thanks from simmy
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2012
    From
    Aus
    Posts
    2

    Re: Equivalence relationships and binary relations

    Dude your a beast, thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 19th 2011, 02:09 PM
  2. binary relations help please :)
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 13th 2010, 09:08 AM
  3. Replies: 10
    Last Post: January 14th 2010, 01:28 PM
  4. Binary Relations
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: September 13th 2009, 11:18 AM
  5. Binary Relations
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: April 13th 2008, 11:41 AM

Search Tags


/mathhelpforum @mathhelpforum