Are there real-life relations which are symmetric and reflexive but not transitive?


$\quad\quad x\;$ has slept with $\;y$ ${}{}{}{}{}$


$x$ lives within one mile of $y$.

This is reflexive and symmetric, but not transitive.


$x$ is indistinguishable from $y$.

The non-transitivity of this relation is my favorite way to account for the non-intuitiveness of the theory of evolution.

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Elementary Set Theory

Relations

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