1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Equivalent sets

  1. Apr 29, 2009 #1
    1. The problem statement, all variables and given/known data

    1. Suppose A-B is equivalent to B-A. show that A is equivalent to B.
    2. if A,B and C are nonempty and A cross B is equivalent to A cross C then B is equivalent to C
    Any help would be appreciated, thanks!

    3. The attempt at a solution
    I tried constructing a bijection, but that did not work out right. Any ideas?
    Last edited: Apr 29, 2009
  2. jcsd
  3. Apr 29, 2009 #2


    Staff: Mentor

    By definition, if two sets A and B are equivalent, that every element in A is also in B, and every element in B is also in A. Can you use this idea on your first problem?

    For your second problem, part of it is missing.
    Is the question "if A,B and C are nonempty and A cross B is equivalent to A cross C, then B is equivalent to C"
  4. Apr 29, 2009 #3
    By equivalent, I mean they have the same cardinality, not that they are equal.
  5. Apr 29, 2009 #4


    Staff: Mentor

    OK, so you know there is an bijection between A - B and B - A. It seems to me there are four cases:
    [tex]A \subset B[/tex]
    [tex]B\subset A[/tex]
    A = B
    [tex]A \cap B = \oslash[/tex]

    Can you eliminate one or more of these as possibilities, and then come up with a bijection for the remaining one(s)?

    Some examples might be helpful to get you thinking in the right way.

    1. A = {2, 4, 6, ...}, B = {1, 2, 3, ...}
    2. A = {2, 3, 4, 5, ...}, B = {1, 2, 3, 4, ...}
    3. any two sets that are equal
    4. A = {2, 4, 6, ... }, B = {1, 3, 5, ... }
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook