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Ordered Pairs in Relation A to B

  1. Feb 13, 2012 #1
    1. The problem statement, all variables and given/known data

    List the ordered pairs in the relation R from A = {1, 2, 3, 5} to B = {2, 4, 6, 9} where <x, y> is an element of R iff:

    (i) x ≥ y
    (ii) x – y < 2
    (iii) x – y > 2
    (iv) l.c.m. (x, y) = 18
    (v) g.c.d. (x, y) = 3


    I understand in general ordered pairs and cartesian products, but I'm not sure where to begin when there are limitations such as these.
     
  2. jcsd
  3. Feb 13, 2012 #2

    tiny-tim

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    welcome to pf!

    hi bird34! welcome to pf! :wink:

    (you understand they're alternatives?)

    what's the difficulty?

    eg for (ii), R = {(5,9),(5,6),(5,4)…}
     
  4. Feb 13, 2012 #3
    I guess maybe I don't understand after all. I get where the numbers came from for (ii), but what about the others ones? I'm lost and need an explanation. Thanks!
     
  5. Feb 13, 2012 #4

    tiny-tim

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    for (ii), R is the set of all ordered pairs (x,y) such that x - y < 2

    so eg 5 - 4 < 2, so (5,4) is in

    but 5 - 2 =3, so (5,2) is out :wink:
     
  6. Feb 13, 2012 #5
    Ok, so for (iii), the answer would only be {5,2}?
     
  7. Feb 13, 2012 #6
    And for (i) it would be R = {2,2}, {3,2}, {5,2}, {5,4}?

    If so, I feel like an idiot for overlooking the simplicity in this!!
    By the way, do you know anything about a digraph?
     
  8. Feb 13, 2012 #7

    tiny-tim

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    yup! :biggrin:
    no, we never did them
    well, that's the only one with x = 5
     
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