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Thread: Is relation transitive or none of them?

  1. #1
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    Question Is relation transitive or none of them?

    Cant draw its mapping either please help
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  2. #2
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    Re: Is relation transitive or none of them?

    It is obviously not reflexive or symmetric, but it is transitive.
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    Re: Is relation transitive or none of them?

    Quote Originally Posted by SlipEternal View Post
    It is obviously not reflexive or symmetric, but it is transitive.
    Please can you draw what the graph would look like for the values?
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  4. #4
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    Re: Is relation transitive or none of them?

    How about you do that? It is going to be a graph with 16 vertices and 3 edges. It should be very straightforward. Look at other examples in your book.

    (Some books may only use 8 vertices and 3 edges)
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    Re: Is relation transitive or none of them?

    It is not "reflexive" because the base set contains "1" but the relationship does not contain "(1, 1)".

    It is not "symmetric" because the relation contains "(a, 1)" but not "(1, a)".

    It is "transitive" since every pair has second member "1" but no pair have first member "1". That is, the is no case where we have "(x, y)" and "(y, z)". The condition for "transitivity" is trivially satisfied.

    For the graph, mark 8 points and label them "1", "2", "3", "4", "5", "a", "b", and "c". Then draw lines connecting "" and "1", "b" and "1", and "c" and "1".
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  6. #6
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    Re: Is relation transitive or none of them?

    Quote Originally Posted by HallsofIvy View Post
    It is not "reflexive" because the base set contains "1" but the relationship does not contain "(1, 1)".

    It is not "symmetric" because the relation contains "(a, 1)" but not "(1, a)".

    It is "transitive" since every pair has second member "1" but no pair have first member "1". That is, the is no case where we have "(x, y)" and "(y, z)". The condition for "transitivity" is trivially satisfied.

    For the graph, mark 8 points and label them "1", "2", "3", "4", "5", "a", "b", and "c". Then draw lines connecting "" and "1", "b" and "1", and "c" and "1".
    Ok thank you done that, how do you know it's transitive for this specific question?
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  7. #7
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    Re: Is relation transitive or none of them?

    Quote Originally Posted by inayat View Post
    Ok thank you done that, how do you know it's transitive for this specific question?
    HallsofIvy answered that for this specific question.

    Quote Originally Posted by HallsofIvy View Post
    It is "transitive" since every pair has second member "1" but no pair have first member "1". That is, the is no case where we have "(x, y)" and "(y, z)". The condition for "transitivity" is trivially satisfied.
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