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Give an example of two relations $R$ and $S$ on $\mathbb{Z}$ with the following properties: (i) both $R$ and $S$ are both symmetric and transitive. (ii) if $\mathcal{R} \subseteq \mathbb{Z} \times \mathbb{Z}$ and $\mathcal{S} \subseteq \mathbb{Z} \times \mathbb{Z}$ represent $R$, respectively $S$, then $$ |\mathcal{R}-\mathcal{S}|=|\mathcal{S}-\mathcal{R}|=1 $$

How does this $1$ come? Don't even have the intuition of $ |\mathcal{R}-\mathcal{S}|=|\mathcal{S}-\mathcal{R}|=1 $.

Really hope someone could help\hint me a little bit!

verret
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Jesse Jin
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1 Answers1

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$\mathcal R=\{(0,0)\},\mathcal S=\{(1,1)\}$.

Kenta S
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