Results 1 to 3 of 3

Thread: Help on a Proof

  1. #1
    Mar 2009

    Help on a Proof

    Hi i have the following question about Cartesian Products:

    Prove, or disprove:

    If A × B = A × C, then B = C.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Mar 2009
    Are you sure it has no restrictions on A?

    If not, then if A=0, then B not necessarily = C. For example, 0*2 = 0*4, 4 not equal 2.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Apr 2005
    tripod87, he said "Cartesian products". A, B, and C are sets, not numbers.

    However, with slightly different notation, the same objection works! (So it is possible that tripod87 meant that but used numerical notation.) If A is the empty set then A X B and A X C are empty for all B and C.

    Suppose A is not empty. If x is any member of B, there exist a pair (a, x) in A X B for some a in A. Since A X B= A X C, that pair is also in A x C. Therefore x is in C. Then B is a subset of C. Can you finish?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: Oct 19th 2010, 10:50 AM
  2. Replies: 0
    Last Post: Jun 29th 2010, 08:48 AM
  3. [SOLVED] direct proof and proof by contradiction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Feb 27th 2010, 10:07 PM
  4. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: Jun 8th 2008, 01:20 PM
  5. proof that the proof that .999_ = 1 is not a proof (version)
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: Apr 14th 2008, 04:07 PM

Search Tags

/mathhelpforum @mathhelpforum