Results 1 to 4 of 4

Math Help - Binary Relations

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    3

    Binary Relations

    I need help with binary relations. The question is which properties do the following binary relations satisfy among the reflexive, symmetric, tansitive, irreflexive, and antisymmetric.

    a. The congruence relation on the set of triangles.
    b. The subset relation on sets.
    c. The relation on people that relates people with bachelor's degrees in computer science.
    e. The "has a common natinal laguage with" relation on countries.
    f. The "is father of " relation on the set of people.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by patches View Post
    I need help with binary relations. The question is which properties do the following binary relations satisfy among the reflexive, symmetric, tansitive, irreflexive, and antisymmetric.
    you know what all these terms mean right? just go through the check list with each part.

    example, for the first.

    a. The congruence relation on the set of triangles.
    Test reflexive:

    is it true that every triangle is congruent to itself? YES. Therefore this relation is reflexive



    Test symmetric:

    is it true that if triangle A is congruent to triangle B, then triangle B is congruent to triangle A (for all triangles A and B)? YES. Thus, this relation is symmetric.



    Test transitive:

    is it true that if triangle A is congruent to triangle B and triangle B is congruent to triangle C, then triangle A will be congruent to triangle C? YES. So the relation is transitive.



    Test Irreflexive:

    We already know the relation is reflexive, so it cannot be irreflexive.


    You could also note (from previous knowledge) that congruence is an equivalence relation, so we know right off the bat it is reflexive, symmetric and transitive. And so cannot be irreflexive.

    Try the others in the same way
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,682
    Thanks
    614
    Hello, patches!

    Here's some help . . .


    Which properties do the following binary relations satisfy
    among: reflexive, symmetric, transitive, irreflexive, and antisymmetric.

    a. The congruence relation on the set of triangles.

     \Delta A \cong \Delta A . . . True: reflexive

    \text{If }\Delta A \cong \Delta B\text{, then }\Delta B \cong \Delta A . . . True: symmetric

    \text{If }\Delta A \cong \Delta B\text{ and }\Delta B \cong \Delta C\text{, then }\Delta A \cong \Delta C . . . True: transitive




    b. The subset relation on sets.

     A \subseteq A . . . True: reflexive

    \text{If }A \subseteq B\text{, then }B \subseteq A . . . not true; not symmetric

    \text{If }A \subseteq B\text{ and }B \subseteq A\text{, then }A = B . . . True: antisymmetric

    \text{If }A \subseteq B\text{ and }B \subseteq C\text{, then }A \subseteq C . . . True: transitive




    e. The "has a common national language with" relation on countries.

    A\:\circledR\:A . . . True: reflexive

    \text{If }A\:\circledR\:B\text{, then }\,B\:\circledR\:A . . . True: symmetric

    \text{If }A\:\circledR\:B\text{ and }B\:\circledR\:C\text{, then }A\:\circledR\:C . . . True: transitive




    f. The "is father of " relation on the set of people.

    A\:\boxed{F }\:A . . . not true: not reflexive

    A\:\boxed{\sim F}\:A . . . true: irreflexive

    \text{If }A\:\boxed{F}\:B\text{. then }B\:\boxed{F}\:A . . . not true: not symmetric

    \text{If }A\:\boxed{F}\:B\text{ and }B\:\boxed{F}\:C\text{, then }A\:\boxed{F}\:C . . . not true: not transitive

    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    This is just picking at whoever wrote this question.
    Would it be true to say that Canada and England have a common national language?
    Would it be true to say that Canada and France have a common national language?
    By law Canada is bilingual.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 19th 2011, 01:09 PM
  2. Binary Relations
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 25th 2011, 07:16 PM
  3. binary relations help please :)
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 13th 2010, 08:08 AM
  4. Binary Relations
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: September 13th 2009, 10:18 AM
  5. binary relations
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: December 15th 2007, 12:56 PM

Search Tags


/mathhelpforum @mathhelpforum