I need a relation which is not reflexive, not symmetric, and not transitive I need an example of a relation which is simultaneously not reflexive, not symmetric, and not transitive.  Any accessible examples?  Thanks in advance.

On $\mathbb{N}$, consider
 $$a \sim b \iff a +2b = 5,$$
then


*

*$1\nsim 1$,

*$3\sim 1$ but $1 \nsim 3$,

*$3\sim 1, 1 \sim 2$ but $3 \nsim 2$.
