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Math Help - a ~ b Relations

  1. #1
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    a ~ b Relations

    I am really struddling to understand these types of questions. Please can someone walkthough it with me.

    The Question is

    On the set N, define a relation ~ by stipulating that a ~ b if
    hcf(a,b) = 1 (where a; b 2 belong to N). Decide if this relation is (a) reflexive, (b) symmetric and
    (c) transitive, in each case giving either a proof or a counterexample, as appropriate.

    Any help would be great thanks
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  2. #2
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    Re: a ~ b Relations

    I think i have managed to do part (a)
    if a~a then hcf(a,a) = a. If a =1,2,3,4,5.... the hcf(a,a)=1,2,3,4,5... Not 1 for all cases. Therefore not reflexive
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  3. #3
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    Re: a ~ b Relations

    Quote Originally Posted by Matt1993 View Post
    The Question is
    On the set N, define a relation ~ by stipulating that a ~ b if
    hcf(a,b) = 1 (where a; b 2 belong to N). Decide if this relation is (a) reflexive, (b) symmetric and (c) transitive, in each case giving either a proof or a counterexample, as appropriate.
    You know that
    8\sim 9~~\&~~9\sim 10 so what does that tell you about transitivity?
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  4. #4
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    Re: a ~ b Relations

    that its not transative because hcf(8,9)=1 and hcf(9,10)=1 but hcf(8,10)= 2
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  5. #5
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    Re: a ~ b Relations

    Quote Originally Posted by Matt1993 View Post
    that its not transative because hcf(8,9)=1 and hcf(9,10)=1 but hcf(8,10)= 2
    That is correct. The relation is symmetric. WHY?
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  6. #6
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    Re: a ~ b Relations

    is it because hcf(a,b) = hcf(b,a) = 1. a and b are both still coprime
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