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How to add sets? easy question?

  1. Sep 5, 2008 #1
    1. The problem statement, all variables and given/known data

    Let A = {-1,2,4,7}
    Let B = {-2,-1,1}

    Find A+B and A*B. (multiply)

    2. Relevant equations

    3. The attempt at a solution

    Am I right here?

    A+B = {-3,-2,0,1,2,3,5,6,8}

    A*B = {-14,-8,-7,-4,-2,-1,1,2,4,7}
    Last edited: Sep 5, 2008
  2. jcsd
  3. Sep 6, 2008 #2
    Sorry this is a bit confusing. I don't think you can add/multiply sets like that. For multiplication you need the cartesian product which is just [tex] (a,b) \quad a\in A, b\in B[/tex]. If you can expand and say what you mean by multiplying and adding sets then I can help a bit more.
  4. Sep 6, 2008 #3


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    Staff Emeritus
    Science Advisor

    There are a number of different ways to define A+ B or A*B for sets. For example, those are often used to mean union and intersection of sets. I think what you are talking about is "z is in A+ B if and only if z= x+ y for some x in A and some y in B" and "z is in A*B if and only if z= xy for some x in A and some y in B." Assuming those are the definitions you are using, yes, what you have is correct.
  5. Sep 6, 2008 #4
    Ahh, so if I defined it as multiplication or addition, then that would be valid.

    Define A + B = [ a + b : a in A, b in B }

    Likewise for A*B. I was confused because it didn't seem natural.
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