Hi, this seems to me like a bit of a silly question, but I've had a problem in set theory given to me, and I'm having trouble working out exactly what it wants - the question word for word is;

Show that the set of all isomorphism classes of relations on $\displaystyle X$ has cardinality less than $\displaystyle 2^{2^{{|X|}^2}}$.

Am I right in taking these isomorphism classes as the sets containing relations $\displaystyle \leq$ and $\displaystyle {\leq}^{\prime}$ such that $\displaystyle (X,\leq)$ is isomorphic to $\displaystyle (X,{\leq}^{\prime})$, or is there some way that relations can themselves be isomorphic, and the isomorphism classes are actually just of isomorphic relations?

I hope the question is clear here!