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Cartesian/cross product proof

  1. Jan 16, 2012 #1
    1. The problem statement, all variables and given/known data

    show for finite sets A,B,that m(A x B ) = m(A)m(B).

    2. Relevant equations

    I don't see relevant equation but we can treat to like cartesian/cross product.


    3. The attempt at a solution

    I tried to think it as (x,y) for m(A x B ) . if we let A = { 1,2} and B= {3,4} then those product will be {1,3},{2,4},{1,4},{1,4} isn't it? but then i am confused with m(A)m(B) because it seems like multiplication .

    I need some hint to prove this statement/question.
    thank you.
     
  2. jcsd
  3. Jan 16, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    m(A)m(B) is multiplication. In your example you listed the elements of the cross product. But you got it wrong. AxB={{1,3},{1,4},{2,3},{2,4}}. There are 4 elements in there. So m(AxB)=4. m(A)=2 and m(B)=2. So m(A)m(B)=2*2=4. So m(AxB)=m(A)m(B).
     
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