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Representation of two relation matrices

  1. Apr 9, 2014 #1
    1. The problem statement, all variables and given/known data

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    3. The attempt at a solution

    I know what relations are individually but what do I do to represent the composition of both? Is it some matrix operation? Would I multiply them, but instead of adding I use the boolean sum?
     
    Last edited: Apr 9, 2014
  2. jcsd
  3. Apr 9, 2014 #2

    Zondrina

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    Let ##R = R_1 \circ R_2 : A → C##

    If you have an element ##a \in A##, how would you be mapping it all the way to ##C## given the two matrices you have?

    Hint: Think about the dimensions of the elements in ##A##.
     
  4. Apr 9, 2014 #3
    I know that I can use the venn diagrams and draw arrows and stuff, but when I multiply the two matrices together, I get the right answer. So will it work for all of them?
     
  5. Apr 9, 2014 #4

    Zondrina

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    Yes, suppose you denote the upper matrix in the problem by ##M_1## and the lower one by ##M_2##.

    According to ##R_1##, you map the elements of ##A## to ##B##. The matrix of the relation happens to be ##M_1##.

    So ##aM_1 \in B##.

    Then to get to ##C##, you multiply by ##M_2##.

    So ##aM_1M_2 \in C##.
     
  6. Apr 9, 2014 #5
    Ahh alright, and I was right to assume that you used the boolean sum, during the multiplicative process?
     
  7. Apr 9, 2014 #6

    Zondrina

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    I believe the question is simply asking you to multiply ##M_1## and ##M_2##. I'm not quite sure what you mean by 'Boolean sum' though.
     
  8. Apr 9, 2014 #7
    If an element of A, a, and an element of B, b, are related then, aRb == 1, so there can only be values of 0 or 1, boolean sum is defined as a logical or so
    0 + 0 = 0
    1 + 0 = 1
    0 + 1 = 1
    1 + 1 = 1
     
  9. Apr 9, 2014 #8

    Zondrina

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    Ahh you intended these as logical matrices. If that's the case then yes.
     
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