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Math Help - Relations proof

  1. #1
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    Relations proof

    Hi guys,

    Can you check my relations proof? It feels correct but at the same it almost seems too easy so I'm wondering if perhaps I missed something.

    Thanks in advance,
    james

    \text{\textbf{Theorem.}} Suppose R is a relation on a set A with the property that for every a \in A,\,aRx for some  x \in A, that is, every element is related to at least one other element in A. Prove that if Ris symmetric and transitive, then R is reflexive.

    \text{\emph{Proof.}} Let a \in A. By hypothesis, aRb for some b \in A. Since R is symmetric, bRa. Since we have that aRb and bRa, and we know that R is transitive, aRa so that R is reflexive.
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  2. #2
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    Your proof is correct.
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