# Equivalence Relations

• May 1st 2009, 10:47 AM
spearfish
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
• May 1st 2009, 11:10 AM
Plato
Both are so simple.
$\begin{gathered}
1 \in \mathbb{Q}^ + \;\& \;\left( {\forall x} \right)\left[ {x^1 = x^1 } \right] \hfill \\
x - x = 0\;\& \;7|0 \hfill \\
\end{gathered}$
• May 1st 2009, 11:14 AM
spearfish
thanks