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Math Help - Equivalence Relations

  1. #1
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    Equivalence Relations

    I am having trouble starting off with the two following problems.


    • Let a R b on Q^+ if and only if a = b^k for some k is an element of Q


    • Let a ~b on Z if and only if 7 divides (a-b)

    Can somebody show me how to prove the reflexive property for each. I can prove symmetric and transitive if I see how to approach each problem. Thanks
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  2. #2
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    Both are so simple.
    \begin{gathered}<br />
  1 \in \mathbb{Q}^ +  \;\& \;\left( {\forall x} \right)\left[ {x^1  = x^1 } \right] \hfill \\<br />
  x - x = 0\;\& \;7|0 \hfill \\ <br />
\end{gathered}
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  3. #3
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    thanks
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