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.

How about:  "is the square of", defined on the set of positive integers?  In other words,
$$a \sim b \iff a=b^2$$
This relation is not reflexive (most numbers are not their own square), not symmetric (if $a$ is the square of $b$ then in most cases $b$ is not the square of $a$) and not transitive (if $a$ is the square of $b$ and $b$ is the square of $c$ then in general $a$ will not be the square of $c$).
