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Math Help - Reflexive and symmetric

  1. #1
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    Reflexive and symmetric

    I was asked to show that the divisibility relation is reflexive, but NOT symmetric.

    Here is what I did...Let me know if it seems acceptable.

    Reflexive:
    Assume a|a, for all a e Z. This implies that a = ac, for some c e Z. Abviously if c = 1, this is true. Thus, it is reflexive.

    Symmetric:
    Assume if a|b, then b|a. I don't know what to do now...

    REMEMBER: Don't get | confused with \. | = Divides and \ = Divided by
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  2. #2
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    For Symmetric you just need to provide a counter example, such as 6/2 = 3 but 2/6 = 1/3 which is not an integer.
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  3. #3
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    Quote Originally Posted by jzellt View Post
    I was asked to show that the divisibility relation is reflexive, but NOT symmetric.
    Reflexive:
    Assume a|a, for all a e Z. This implies that a = ac, for some c e Z. Abviously if c = 1, this is true. Thus, it is reflexive.
    If your set is Z then the relation is not reflexive.
    Zero does not divide zero.
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