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Math Help - please help with discrete math

  1. #1
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    please help with discrete math

    Which properties do each of the following relations satisfy among the properties relexive, symmetric transitiv, irreflexive, and antisymmetric?

    1. R = {(a,b) l a squared = b squared} over the real numbers

    2. R = {(x,y) l x divides y} over the positive integers


    For each of the following conditions, find the smallest relation over the set A = {a,b,c} that satisfies the stated properties.

    1. symmetric, not reflexive, not transitive

    2. reflexive and symmetric, but not transitive

    For each of the following properties, find a binary relation R such that R has the property but R squared does not.

    1. Antisymmetric

    Given the relation "less" over the natural numbers N, descre each of he following compositions as a set of the form {(x,y) l property}.

    1. less less less
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  2. #2
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    Hello, patches!

    Here's some help . . .


    Which properties do each of the following relations satisfy among the properties:
    relexive, symmetric transitive, irreflexive, and antisymmetric?

    1)\;\;R \:= \:\{(a,b)\:|\:a^2= b^2\} over the real numbers

    a^2\,=\,a^2 . . . True: reflexive

    \text{If }a^2 \,=\,b^2\text{, then }b^2\,=\,a^2 . . . True: symmetric

    \text{If }a^2\,=\,b^2\text{ and }b^2\,=\,c^2\text{, then }a^2\,=\,c^2 . . . True: transitive





    2)\;\;R \:= \: \{(x,y)\:|\:x\text{ divides }y\} over the positive integers

    a\:\boxed{D}\:a . . . True: reflexive

    \text{If }a\:\boxed{D}\:b\text{, then }b\:\boxed{D}\:a . . . False: not symmetric

    \text{If }a\:\boxed{D}\:b\text{ and }b\:\boxed{D}\:a\text{, then }a = b . . . True: antisymmetric

    \text{If }a\:\boxed{D}\:b\text{ and }b\:\boxed{D}\:c\text{, then }a\:\boxed{D}\:c . . . True: transitive


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  3. #3
    Lord of certain Rings
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    For each of the following conditions, find the smallest relation over the set A = {a,b,c} that satisfies the stated properties.

    1. symmetric, not reflexive, not transitive

    2. reflexive and symmetric, but not transitive
    1. a \neq b or a nicer one, gcd(a,b) = 1;

    2. this one's tricky, try gcd(a,b) = max(a,b)
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