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Math Help - relation question

  1. #1
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    relation question

    let R be a relation on real numbers that is symmetric and transitive.
    prove that if Dom(R) = real numbers then R is reflexive.

    Can someone help me out with this please?
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  2. #2
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    Re: relation question

    Hint: Can you make two steps and come to your initial position?

    Of course, real numbers are irrelevant here. What matters is that for every $x$ there exists a $y$ such that $xRy$, i.e., $\operatorname{dom} R$ is the whole set on which $R$ is defined.
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  3. #3
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    Re: relation question

    Proof:
    Let R be a relation on R that is symmetric and transitive.
    Suppose Dom(R) = R.
    Consider real number x.
    Since x is in Dom(R) = R, there exists y in R such that xRy.
    Since R is symmetric, yRx.
    Since R is transitive, xRx.
    Thus, for all x in R, xRx.

    Therefore, R is reflexive.
    Last edited by Convrgx; July 13th 2014 at 01:50 PM.
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