Is a relation $R$ on a set $X$ a set?

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I'm reading Set Theory by Thomas Jech.

An n-ary relation $R$ is a set of $n$-tuples. $R$ is a relation on $X$ if $R \subset X^n$.

I tried to conclude that a relation $R$ on a set $X$ is a set using Separation Schema

$$\forall X \forall p \exists Y \forall u (u \in Y \leftrightarrow u \in X \land \varphi(u, p))$$

Although it will be trivial when $X$ is a finite set(by enumerating each of the tuples), I think it's difficult to construct such a formula $\varphi(u,p)$ according to $R \subset X^n$ when $X$ is an infinite set.

Appreciate your help in advance, thanks.