Results 1 to 2 of 2

Math Help - functions proof (is it right?)

  1. #1
    Member pberardi's Avatar
    Joined
    Dec 2008
    Posts
    85

    functions proof (is it right?)

    Prove that if
    g: A -> B is 1-1
    f: B -> C is 1-1
    then fog: A -> C is 1-1

    pf.
    Need to show that if f(g(a)) = f(g(c)) then a = c for fog to be 1-1

    Because g is 1-1, g(a) = g(b) and a = b
    Because f is 1-1, f(b) = f(c) and b = c therefore a = c
    Therefore since a = c, fog is a 1-1 function.
    Last edited by pberardi; May 10th 2009 at 01:43 PM. Reason: grammar
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,677
    Thanks
    1618
    Awards
    1
    Quote Originally Posted by pberardi View Post
    Prove that if
    g: A -> B is 1-1
    f: B -> C is 1-1
    then fog: A -> C is 1-1

    pf.
    Need to show that if f(g(a)) = f(g(c)) then a = c for fog to be 1-1

    Because g is 1-1, g(a) = g(b) and a = b
    Because f is 1-1, f(b) = f(c) and b = c therefore a = c
    Therefore since a = c, fog is a 1-1 function.
    It should be:
    \begin{gathered}<br />
  f \circ g(a) = f \circ g(a) \hfill \\<br />
  g(a) = g(a)\;,\;f~\text{is one-to-one} \hfill \\<br />
  a = b\;,\;g ~\text{is one-to-one}\hfill \\ <br />
\end{gathered}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A functions proof
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: August 12th 2010, 02:10 AM
  2. Proof regarding 1-1 functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 15th 2009, 03:54 PM
  3. Proof using functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 15th 2009, 12:25 PM
  4. Functions Proof
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 1st 2009, 05:42 PM
  5. Proof regarding functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 13th 2009, 08:42 PM

Search Tags


/mathhelpforum @mathhelpforum