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Math Help - Binary Relations

  1. #1
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    Binary Relations

    I have a question here that states:

    With a table like that in Fig. 2.2, illustrate a relation on the set {a,b,c,d} that is:

    i) not symmetric and not antisymmetric
    and ii) transitive

    (the table in question is your basic 5x5 table which abcd in both the x and y axis, and the corresponding relations are checked off in the boxes)

    I thought about it and resulted in:

    i) {(a,a), (b,b), (c,b), (c,c)} --> does this make sense?

    and for ii) could i just put: {(a,a), (b,b), (c,c), (d,d)}?

    Any help would be greatly appreciated. Thanks.
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  2. #2
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    Quote Originally Posted by GreenDay14 View Post
    illustrate a relation on the set {a,b,c,d} that is:
    i) not symmetric and not antisymmetric
    and ii) transitive
    I thought about it and resulted in:

    i) {(a,a), (b,b), (c,b), (c,c)} --> does this make sense?
    That is not symmetric. Did you mean (b,c)?
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    Yes I did sorry. I think I arrived at the right answer for that one. It's the second one that is really confusing me.
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  4. #4
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    Your second is correct.
    The diagonal of any set, \Delta_A, is an equivalence relation.
    Therefore, it must be transitive.
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  5. #5
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    Thank you very much for your help.
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