$X = \mathbb{Z}^+$ and $R$ is the relation defined by $nRm$ if and only if there is a non-zero $k \in \mathbb{Q}$ for which $n^k = m$. Is this relation anti-symmetric? Explain.
I'm pretty sure it isn't, but I don't know how to justify it.
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It is symmetric because $n=m^{\frac{1}{k}}$. – John Douma Oct 30 '18 at 03:54
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But k can also be negative so wouldn't it still not be symmetric? – George Oct 30 '18 at 03:57
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That is not hard to fix. – John Douma Oct 30 '18 at 04:00
1 Answers
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$4,2 \in \mathbb{Z+}$
$2 = 4^{\frac{1}{2}}$ and $ 4 = 2^{2}$
Then $2R4$ and $4R2$ but $2 \not= 4$
Then isn't anti-symmetric
ZAF
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