(Logic) can a set be both reflexive and asymmetric?

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I am just starting to learn logic at undergraduate level.



My exercise book is asking me to: "Specify a relation and a set $S$ such that the relation is reflexive on $S$ and asymmetric".



How can a set be both reflexive and asymmetric?






elementary-set-theory logic relations







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    up vote
    4
    down vote

    favorite












    I am just starting to learn logic at undergraduate level.



    My exercise book is asking me to: "Specify a relation and a set $S$ such that the relation is reflexive on $S$ and asymmetric".



    How can a set be both reflexive and asymmetric?






    elementary-set-theory logic relations







    share|cite|improve this question









    New contributor




    Hugo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.





















      up vote
      4
      down vote

      favorite









      up vote
      4
      down vote

      favorite











      I am just starting to learn logic at undergraduate level.



      My exercise book is asking me to: "Specify a relation and a set $S$ such that the relation is reflexive on $S$ and asymmetric".



      How can a set be both reflexive and asymmetric?






      elementary-set-theory logic relations







      share|cite|improve this question









      New contributor




      Hugo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      I am just starting to learn logic at undergraduate level.



      My exercise book is asking me to: "Specify a relation and a set $S$ such that the relation is reflexive on $S$ and asymmetric".



      How can a set be both reflexive and asymmetric?






      elementary-set-theory logic relations




      elementary-set-theory logic relations






      share|cite|improve this question









      New contributor




      Hugo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question









      New contributor




      Hugo is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|cite|improve this question




      share|cite|improve this question








      edited 4 hours ago









      Taroccoesbrocco

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          Suppose $S$ is non-empty. Take an element $ain S$; since the relation is reflexive $asim a$. Yet since the relation is asymmetric, this implies $anotsim a$, which is absurd.



          We get around this by specifying $S=varnothing$ and the relation as the empty relation. It is vacuously reflexive and asymmetric.






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          • Excellent thank you so much
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            @Hugo Now accept my answer (click on the tick below the score on the left of my answer) and we'll be done with this.
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          up vote
          5
          down vote













          Suppose $S$ is non-empty. Take an element $ain S$; since the relation is reflexive $asim a$. Yet since the relation is asymmetric, this implies $anotsim a$, which is absurd.



          We get around this by specifying $S=varnothing$ and the relation as the empty relation. It is vacuously reflexive and asymmetric.






          share|cite|improve this answer




















          • Excellent thank you so much
            – Hugo
            3 hours ago






          • 2




            @Hugo Now accept my answer (click on the tick below the score on the left of my answer) and we'll be done with this.
            – Parcly Taxel
            3 hours ago














          up vote
          5
          down vote













          Suppose $S$ is non-empty. Take an element $ain S$; since the relation is reflexive $asim a$. Yet since the relation is asymmetric, this implies $anotsim a$, which is absurd.



          We get around this by specifying $S=varnothing$ and the relation as the empty relation. It is vacuously reflexive and asymmetric.






          share|cite|improve this answer




















          • Excellent thank you so much
            – Hugo
            3 hours ago






          • 2




            @Hugo Now accept my answer (click on the tick below the score on the left of my answer) and we'll be done with this.
            – Parcly Taxel
            3 hours ago












          up vote
          5
          down vote










          up vote
          5
          down vote









          Suppose $S$ is non-empty. Take an element $ain S$; since the relation is reflexive $asim a$. Yet since the relation is asymmetric, this implies $anotsim a$, which is absurd.



          We get around this by specifying $S=varnothing$ and the relation as the empty relation. It is vacuously reflexive and asymmetric.






          share|cite|improve this answer












          Suppose $S$ is non-empty. Take an element $ain S$; since the relation is reflexive $asim a$. Yet since the relation is asymmetric, this implies $anotsim a$, which is absurd.



          We get around this by specifying $S=varnothing$ and the relation as the empty relation. It is vacuously reflexive and asymmetric.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 4 hours ago









          Parcly Taxel

          34.3k136890




          34.3k136890











          • Excellent thank you so much
            – Hugo
            3 hours ago






          • 2




            @Hugo Now accept my answer (click on the tick below the score on the left of my answer) and we'll be done with this.
            – Parcly Taxel
            3 hours ago
















          • Excellent thank you so much
            – Hugo
            3 hours ago






          • 2




            @Hugo Now accept my answer (click on the tick below the score on the left of my answer) and we'll be done with this.
            – Parcly Taxel
            3 hours ago















          Excellent thank you so much
          – Hugo
          3 hours ago




          Excellent thank you so much
          – Hugo
          3 hours ago




          2




          2




          @Hugo Now accept my answer (click on the tick below the score on the left of my answer) and we'll be done with this.
          – Parcly Taxel
          3 hours ago




          @Hugo Now accept my answer (click on the tick below the score on the left of my answer) and we'll be done with this.
          – Parcly Taxel
          3 hours ago










          Hugo is a new contributor. Be nice, and check out our Code of Conduct.









           

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