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Math Help - reflexive and irreflexive relation

  1. #1
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    reflexive and irreflexive relation

    can you explain me the difference between refflexive and irreflexive relation
    and
    can a relation on a set br neither reflexive nor irreflexive
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  2. #2
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    Re: reflexive and irreflexive relation

    Quote Originally Posted by annie12 View Post
    can you explain me the difference between refflexive and irreflexive relation
    and can a relation on a set be neither reflexive nor irreflexive
    Consider A=\{a,b,c\} and :
    \\\mathcal{R}_1=\{(a,a),(b,b),(c,c),(a,b),(b,c)\},  \\\mathcal{R}_2=\{(a,b),(b,c),(c,a)\},~\&\\ \mathcal{R}_3=\{(a,a),(c,c),(a,b),(b,c)\}

    The relation \mathcal{R}_1 is reflexive because each element is related to itself.

    The relation \mathcal{R}_2 is irreflexive because no element is related to itself.

    The relation \mathcal{R}_3 is neither reflexive nor irreflexive. WHY?
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  3. #3
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    Re: reflexive and irreflexive relation

    in R1 (a,b),(b,c) is not related to its self so how can u say it is reflexive
    and in R3 (a,b)(b,c) is a part of irreflexive relation so how how it is nor irreflexive
    please explain me the if i am right or wrong
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