Results 1 to 3 of 3

Thread: inverse image question, is it correct?

  1. #1
    Junior Member
    Joined
    Apr 2009
    Posts
    55
    Thanks
    1

    inverse image question, is it correct?

    Let $\displaystyle X$ and $\displaystyle Y$ be sets , let $\displaystyle A \subseteq X$ and $\displaystyle B$ $\displaystyle \subseteq Y$, and let $\displaystyle f:X \times Y \longrightarrow X$ be a projection map.

    Show that $\displaystyle f^{-1}(A) = A \times Y$.


    I wonder if the question is correct. For example, let $\displaystyle X $= {1, 2} and $\displaystyle Y$ = {a,b}. Then, $\displaystyle X \times Y$ = {(1,a), (1,b), (2,a), (2,b)}.

    Suppose $\displaystyle f(1,a)= f(1,b)=f(2,a)=2,$ and $\displaystyle f(2,b)=1$.

    Suppose $\displaystyle A $= {1} $\displaystyle \subseteq$ {1,2} = $\displaystyle X$.

    Then $\displaystyle f^{-1}(A) $= {(2,b)}$\displaystyle \neq A \times Y$ = {(1,a), (1,b)}.

    Please check whether I am right that the proposition was wrong from the question.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,796
    Thanks
    2827
    Awards
    1
    Quote Originally Posted by armeros View Post
    Let $\displaystyle X$ and $\displaystyle Y$ be sets , let $\displaystyle A \subseteq X$ and $\displaystyle B$ $\displaystyle \subseteq Y$, and let $\displaystyle f:X \times Y \longrightarrow X$ be a projection map. Show that $\displaystyle f^{-1}(A) = A \times Y$.

    I wonder if the question is correct. For example, let $\displaystyle X $= {1, 2} and $\displaystyle Y$ = {a,b}. Then, $\displaystyle X \times Y$ = {(1,a), (1,b), (2,a), (2,b)}.
    You have the projection wrong.
    $\displaystyle f_x(1,a)=f_x(1,b)=1~\&~f_x(2,a)=f_x(2,a)=2$.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2009
    Posts
    55
    Thanks
    1
    Oh, how careless I am.

    I thought a projection is just another name for a function. The way I define in my inquiry was to define a function, not a projection.

    Sorry to bother you with such a careless question.

    Thanks a lot!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inverse image of a function defined on R
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Oct 12th 2011, 02:05 AM
  2. Image and Inverse Images for Projection Functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Apr 20th 2010, 09:56 PM
  3. image sets and inverse set
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Apr 20th 2010, 12:01 PM
  4. A question about image of inverse functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Oct 29th 2009, 08:30 AM
  5. Prove that the inverse image of V is a subspace in X.
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: Jun 22nd 2008, 01:25 AM

Search Tags


/mathhelpforum @mathhelpforum