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Scalar multiplying a set?

  1. Dec 5, 2012 #1
    Scalar multiplying a set??

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

    Let A and B be two finite non-empty sets such that A [itex]\subset[/itex] B and n({C : C [itex]\subset[/itex] B\A}) = 128. Then what is the value of n(B) - n(A)?

    2. Relevant equations



    3. The attempt at a solution

    I actually got to 7 by assuming that n was multiplying the cardinality of C, but I am not sure if that is what happens. What does it mean to have a scalar multiplying a set? Or is n not a scalar in this case?
     
  2. jcsd
  3. Dec 5, 2012 #2

    Mark44

    Staff: Mentor

    Re: Scalar multiplying a set??

    I don't read this as "n times a set" but as "the number of elements in set <whatever>". Check your book or notes for exactly what this notation means.
     
  4. Dec 5, 2012 #3
    Re: Scalar multiplying a set??

    That actually makes a lot of sense! I checked my book and n(A) is a notation for the cardinality of A. But the funny thing is that the answer would still be 7, even though I carried the notation around as if it were a multiplication.

    If C = P(B\A) where P(B/A) is the power set of B\A. Then n(C : {C [itex]\subset[/itex] A\B}) = P(B\A) = 2n(B\A) = 128 = 27.

    Therefore n(B\A) = 7.

    n(B\A) = n(B) - n(A) if A [itex]\subset[/itex] B.

    Is that still correct?
     
  5. Dec 5, 2012 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Scalar multiplying a set??

    Yes, it is. I'm not sure how you got it by misunderstanding the notation, but ok.
     
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