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Thread: Relation that is 1-1, reflexive, but not symmetric

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    Relation that is 1-1, reflexive, but not symmetric

    Lets say a set A has seven elements . Can a relation on A be 1-1, reflexive, but not symmetric?

    I say no its impossible cause in order to be not symmetric and reflexive we would have to use an element in the domain more than once and that would not make it 1-1.

    What do you think?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: Relation that is 1-1, reflexive, but not symmetric

    If R\subset A\times A is reflexive, then (a,a)\in R for all a\in A . If R is one to one, then (a,b)\in R and (a,c)\in R implies b=c that is, necessarily R=\Delta=\{(a,a):a\in A\} . This means that R is the equality relation on A (equivalence relation).
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    Re: Relation that is 1-1, reflexive, but not symmetric

    So no?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: Relation that is 1-1, reflexive, but not symmetric

    Quote Originally Posted by Aquameatwad View Post
    So no?
    Yes, no.
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