DSE 2020 Question 16: Sets, relations and functions

Let a binary relation $\succ$ on a set $X$ be asymmetric (for all $x,y$: $x\succ y$ implies $\lnot(y\succ x)$) and negatively transitive (for all $x,y,z$: $x\succ y$ implies $x\succ z$ or $z\succ y$). Recall $\succ$ is irreflexive if $\lnot(x\succ x)$ for all $x$, and transitive if $x\succ y$ and $y\succ z$ imply $x\succ z$. Then $\succ$ is