Results 1 to 3 of 3

Math Help - Discrete Math Relations

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    2

    Discrete Math Relations

    Hi,

    If a relation is reflexive, symmetric, and transitive; it would mean that the relation is also an equivalence relation? That's my understanding, if I am wrong please correct me.

    Say:
    R= {(a,a),(a,b),(a,c),(b,a),(b,b),(b,c),(c,a),(c,b),( c,c),(d,d),(d,e),(e,d),(e,e),(f,f)}


    From this relation I believe that "All except (a,a) , (b,b), (c,c), (d,d), (e,e), (f,f) are equivalence relations"...is that correct or no. I'm not catching on to the whole reflexive, symmetric and transitive part.

    The only relation I understand 100% is that transitive is a is the mother of b and b is the mother of c, meaning a is the grandmother of c so it is transitive?

    Thanks for any help!

    Dan
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Jan 2009
    Posts
    58
    That is correct. An equivalence relation must be reflexive, symmetric and transitive.

    Your relation, however, is R. That means R must be reflexive, symmetric and transitive because R represents a relation on {a, b, c, d, e, f}. You do not imply assign the individual pairs as being symmetric etc. It must be the entire relation.

    R= {(a,a),(a,b),(a,c),(b,a),(b,b),(b,c),(c,a),(c,b),( c,c),(d,d),(d,e),(e,d),(e,e),(f,f)}

    A relation is reflexive if it contains all pairs of the form (a,a). Therefore, if R represents a relation on {a,b,c,d,e,f} it must contain (a,a), (b,b), (c,c), (d,d), (e,e) and (f,f), which your relation does.

    To test for symmetry, you have to make sure no pair in the relation without the opposite. Meaning is (a,b) is in the relation, you must also have (b,a). Your relation is symmetric.

    A relation is transitive if if whenever the relation contains (a,b) and (b,c), it also contains (a,c). This also menas that if it contains the pairs (a,b) and (b,a), it must also have (a,a) and (b,b). Your relation R is therefore also transitive and a equivalence relation.

    I hope this helps!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2009
    Posts
    108
    Transitive would mean:

    If a is b's mom, and b is c's mom, then a is c's mom.

    I don't think this is going to hold true.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Discrete math
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 7th 2009, 10:30 PM
  2. discrete math help please
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 7th 2009, 05:10 PM
  3. Discrete Relations
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: April 15th 2008, 02:56 PM
  4. New To Discrete Math - HELP :(
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: January 17th 2008, 10:56 AM
  5. help on discrete math,please?:-)
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 8th 2008, 04:33 AM

Search Tags


/mathhelpforum @mathhelpforum