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Proving a subset of a cartesion cross product

  1. Nov 6, 2007 #1

    ar6

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    1. The problem statement, all variables and given/known data

    A, B, C and D are sets

    if A x B is a subset of C x D then A is a subset of C and B is a subset of D.


    3. The attempt at a solution

    My attempt by contraposition.

    Assume A is not a subset of C or B is not a subset of D. There exists an 'a' which is an element of A but is not an element of C and there exists a 'b' that is an element of B but not an element of D. 'a,b' is an element of A x B but 'a,b' is not an element of C x D. Therefore, A x B is not a subset of C X D. Thus, by contraposition, if A x B is a subset of C x D then A is a subset of C and B is a subset of D.
     
  2. jcsd
  3. Nov 6, 2007 #2

    mjsd

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    Homework Helper

    looks ok to me. but I must say I am a bit rusty on this kind of proofs these days. when I have more time, I may return and check it again.

    EDIT: on 2nd thought, it still looks good to me :smile:
     
    Last edited: Nov 6, 2007
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