Results 1 to 2 of 2

Thread: Proving an equation

  1. October 13th 2009, 07:01 PM #1
    6DOM
    6DOM is offline
    Junior Member
    Joined
    Sep 2009
    Posts
    26

    Proving an equation



    My textbook says this is obvious, but I don't see how it is

    How is this true?

    Thanks
    Follow Math Help Forum on Facebook and Google+
  2. October 13th 2009, 07:12 PM #2
    redsoxfan325
    redsoxfan325 is offline
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    Quote Originally Posted by 6DOM View Post


    My textbook says this is obvious, but I don't see how it is

    How is this true?

    Thanks
    Proof of f^{-1}(A^c)\subseteq(f^{-1}(A))^c:

    x\in f^{-1}(A^c)\implies f(x)\in A^c\implies f(x)\notin A\implies x\notin f^{-1}(A)\implies x\in(f^{-1}(A))^c

    For the other direction, just flip the implication arrows. (This reasoning works in both directions.)
    Follow Math Help Forum on Facebook and Google+
« Non normal Cover | Prove Compactness - Directly from definition »

Similar Math Help Forum Discussions

  1. proving equation
    Posted in the Statistics Forum
    Replies: 2
    Last Post: December 19th 2011, 05:35 AM
  2. Proving this equation?
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 26th 2011, 10:00 PM
  3. Proving an equation.
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: August 9th 2010, 05:14 AM
  4. Proving the equation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 8th 2010, 10:49 PM
  5. Proving the log equation
    Posted in the Algebra Forum
    Replies: 5
    Last Post: January 9th 2010, 03:58 AM

Search Tags


/mathhelpforum @mathhelpforum