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Homework Help: Finite sets homework problem

  1. Feb 5, 2005 #1
    sets A and B. A cross B not equals the empty set. Prove that A or B is finite.

    I think that you can't... don't ask me for my work because I have none.
     
  2. jcsd
  3. Feb 5, 2005 #2
    I agree.

    The regular x,y coordinate system is a cross product of real numbers. Each ordered pair is an element of the cross product and it is not the empty set and yet set A = set B and set A is not finite.
     
  4. Feb 5, 2005 #3
    If anyone thinks that it can be proved, then just say that it can be and give me a hint in the right direction please.

    Thanks for peeking in.
     
  5. Feb 5, 2005 #4
    I thought I just gave you a counter example. Your statement is basically a universally quantified statement for sets, unless I am reading it wrong, and so just a single counter example is sufficient to prove that it is not true. You cannot prove something is true if it is not true. I am not a expert on set theory but in this case it seems pretty straight foreword, no?

    Best of luck...
     
  6. Feb 5, 2005 #5
    Sorry, but I am a total noob with sets. I see it as, if they ask you to prove something then it must be true; atleast it was true for all the other question.

    As for this question I think that there is not enough info to conclude anything about A or B besides that none of them is an empty set. :confused: :grumpy: I've reread the set section and there is nothing about what makes a set finite(I do know what a finite set is).
     
  7. Feb 5, 2005 #6
    If the question said

    A cross B is not the empty set, prove that there exist at least one case where set A or set B is finite, then you could but prove there is at least one case by showing one example. No problem

    A={x,y} and B={r,s}

    So A cross B is just

    {(x,r),(x,s),(y,r),(y,s)}

    QED.

    But your question asked in us to prove this is true for all sets A and B. How can you prove something that is not true?

    I think you must have the question wrong because it really does not make much sense. I bet it asked to prove that if A or B is finite then A cross B is finite. Maybe you could look at the question one more time and make sure you got it right.

    Best of luck
     
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