1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Counterexample for set identity

  1. Jun 20, 2011 #1

    WannabeNewton

    User Avatar
    Science Advisor

    1. The problem statement, all variables and given/known data
    Consider the function [tex]f:X \to Y[/tex]. Suppose that A and B are subsets of X. Decide whether the following statements are necessarily true (I am including just the one I had trouble with):
    (a) if [tex]A\cap B = \emptyset [/tex], then [tex]f[A]\cap f = \emptyset [/tex]

    2. Relevant equations



    3. The attempt at a solution
    I know this statement is false and I know I have to use a counter example. The problem is I am not at all good with counter examples. Could I use a discrete situation as a way of disproving the statement? For example, if I let [tex]X = \mathbb{R}[/tex], A = {-1, -2, -3}, B = {1, 2, 3}, and f = {(x,y): y = x^2} then [tex]A\cap B = \emptyset [/tex] but f[A] = f = {1, 4, 9} so [tex]f[a]\cap f\neq \emptyset [/tex]. I don't know if this suffices as a counter example because it is a very specific example so I was hoping you guys could help me come up with one that would be credible?
     
    Last edited: Jun 20, 2011
  2. jcsd
  3. Jun 20, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    There's nothing wrong with a counterexample being specific. That looks fine to me.
     
  4. Jun 20, 2011 #3

    WannabeNewton

    User Avatar
    Science Advisor

    Oh ok. Thank you.
     
  5. Jun 20, 2011 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    The LaTeX symbol for the emptyset is simply \emptyset
     
  6. Jun 20, 2011 #5

    WannabeNewton

    User Avatar
    Science Advisor

    Fixed it thanks mate.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Counterexample for set identity
  1. Set Theory Identities (Replies: 1)

  2. Proving a set identity (Replies: 1)

Loading...