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Math Help - discrete math relations simple problems help !!!!

  1. #1
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    discrete math relations simple problems help !!!!

    hello everyone

    pllz give me the final result for these problems ???!!!!


    discrete1.bmp
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: discrete math relations simple problems help !!!!

    What have you tried? What's the definition of a relation? Reflexive relation? Symmetric relation? Transitive relation?
    Showe some work.
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  3. #3
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    Re: discrete math relations simple problems help !!!!

    I know them and they are
    Reflexive relation R on A, if ∀a ∈ A, (a, a) ∈ R.
    Symmetric relation R on A, if ∀a∀b ∈ A, (a, b) ∈ R → (b, a) ∈ R.
    Antisymmetric relation R on A, if ∀a∀b ∈ A, (a, b) ∈ R ^ (b, a) ∈ R → a=b.
    Transitive relation R on A, if ∀a∀b∀c ∈ A, (a, b) ∈ R ^ (b, c) ∈ R → (a, c) ∈ R.

    In the second question A) it's every thing except antisymmetric
    b) is symmetric only

    In the first one A) 2^16
    B)2^12 , 2^10

    Am I right ???
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    Re: discrete math relations simple problems help !!!!

    Quote Originally Posted by ujnikm View Post
    In the first one A) 2^16
    B)2^12 , 2^10
    Am I right ???

    The answer to A) depends on your textbook. It may be 2^{12}-1 because some authors do not allow an empty relation.


    The answer to B) depends on how you are reading the question.
    I read it as, "How many relations are reflexive and symmetric.
    That would be 2^6.

    But there are 2^{12} reflexive relations.
    And there are 2^{10} symmetric relations.
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