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Math Help - Relations

  1. #1
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    Relations

    Let R be a relation on positive Z defined as follows:

    for all a, b as a member of positive Z, aRb if and only if a/b = 2 raised to the i for some integer i.

    (a) Prove R is a equivalence relation.
    (b) Find 3 members of the equivalence class of 60.

    To show that R is an equivalence relation, I must show that it's reflexive,symmetric and transitive:

    R is reflexive if and only if aRa:

    a/a = 2 raised to the i

    But we know: a/a = 1, and I don't know how to prove that R is reflexive.

    R is symmetric aRb and bRa

    a/b = 2 raised to the i and b/a= 2 raised to the i

    We can suppose a/b = 2 raised to the i and then try to show that b/a= 2 raised to the i, but thats as far as i've gotten

    when R is transitive I'm at a loss...


    ALSO, i dont know how to get the equivalency class 60 when its not in the set of numbers 2 raised to the i

    help...
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  2. #2
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    Quote Originally Posted by luckyNUM7 View Post
    Let R be a relation on Z^+ defined as follows: for all a, b in Z^+, aRb if and only if a/b = 2 raised to the i for some integer i.
    (a) Prove R is a equivalence relation.
    (b) Find 3 members of the equivalence class of 60.
    Note that i can be any integer.
    So to prove the relation is reflexive let i=0 because 2^0=1.

    Symmetry is as easy: if \frac{a}{b}=2^j then \frac{b}{a}=2^{-j}.

    You do transitivity.

    Because \frac{60}{15}=2^2, you now at least one member of R_{[60]}.
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