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Question about notation?

  1. Jun 24, 2011 #1
    1. The problem statement, all variables and given/known data
    Let R be a relation defined in a set A

    If for all [itex] x \in A [/itex] we have x R x, we call R reflexive
    what does it mean when they write x R x ?


    And
    if for all x,y,z in A we have (x R y and y R z) --> x R z, we call R transitive .
    Im not sure what they mean by transitive
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 24, 2011 #2

    LCKurtz

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    Let's look at a couple examples. Let A be the natural numbers. Let's define a relation R by saying mRn if m divides n. Let's see if it reflexive and transitive. To check reflexive we need:

    For all n in A, nRn, which means n divides n. Obviously true, so this R is reflexive.

    To check transitive we need if nRm and mRp then nRp, which in this case means:
    If n divides m and m divides p, then n divides p. Can you see that is true so R is transitive.

    Now look at a new R defined by mRn means m < n. Can you see this R is not reflexive but it is transitive? Does that help?
     
  4. Jun 24, 2011 #3
    if m<n then n cant be less than m . so is that why it is not reflexive?
    But it is transitive because m<n and there is another # such that m<n<z
     
  5. Jun 24, 2011 #4

    Dick

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    That m<n and n<m can't both be true proves it's not SYMMETRIC. It's not REFLEXIVE because n<n isn't true. Do you see how that's related to the x R x?
     
    Last edited: Jun 24, 2011
  6. Jun 24, 2011 #5
    I think i see now, how do we pronounce x R x
    and also is this set transitive {(1,2), (2,3) , (1,3 )}
     
    Last edited: Jun 24, 2011
  7. Jun 24, 2011 #6

    Dick

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    "x is related by R to x". If R is "less than" than "x is less than x". If R is "divisible" then "x is divisible by x".
     
  8. Jun 25, 2011 #7
    ok thanks for your response .
    I was just wondering if this set I made up was transitive. to check my understanding.
    and also is this set transitive {(1,2), (2,3) , (1,3 )}
     
  9. Jun 25, 2011 #8

    Dick

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    Yes, it is.
     
  10. Jun 25, 2011 #9
    ok i think i understand now,
     
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