Results 1 to 2 of 2

Math Help - Abstract Algebra

  1. #1
    Junior Member
    Joined
    Aug 2008
    Posts
    44

    Abstract Algebra

    Let A and B be sets and let f: A --> B be a function.
    Define a relation on A as follows. If a,b in A, we say that aRb if and only if there exists some c in B such that f(a) = c and f(b) = c. Prove that R is and equivalence relation on A.

    Ok, I know that i need to show the 3 properties. transitive, symmetry, and reflexsive. I also notice that f(a)=f(b). can i assume that a=b?

    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,925
    Thanks
    1764
    Awards
    1
    Quote Originally Posted by Juancd08 View Post
    Let A and B be sets and let f: A --> B be a function. Define a relation on A as follows. If a,b in A, we say that aRb if and only if there exists some c in B such that f(a) = c and f(b) = c. Prove that R is and equivalence relation on A. Can i assume that a=b?
    Absolutely not. That would imply the f is injective.
    However, this is an easy problem if one understands the set theoretical definition of functions.
    The three necessary properties just ‘fall’ out of that definition.
    For example, f(a)=f(a)=c means that aRa, reflexive.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: December 6th 2010, 04:03 PM
  2. Replies: 0
    Last Post: April 24th 2010, 12:37 AM
  3. Abstract Algebra
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 22nd 2008, 06:21 PM
  4. abstract algebra
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 4th 2008, 07:00 PM
  5. Abstract Algebra help
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 12th 2008, 02:59 AM

Search Tags


/mathhelpforum @mathhelpforum