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The question is, "Show that the relation R = ∅ on the empty set S = ∅ is reflexive, symmetric, and transitive."

I was told by my teacher that you could simply say it can't be shown that each property isn't true; and that would show that the relation had those three properties. To me, this answer isn't very satisfying. Could someone, perhaps, elaborate on this idea more?

Thank you!

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To show reflexivity, note that for every $x\in\varnothing$, we have $xRx$.

To show symmetry, note that for every $x,y\in\varnothing$, we have $xRy$ implies $yRx$.

To show transitivity, note that for every $x,y,z\in\varnothing$, we have $xRy$ and $yRz$ implies $xRz$.

These are vacuously true because the empty set contains no elements.

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    + 1 for the exposition!2012-11-23