# how to convert sentence that contains “no more than 3” into predicate logic sentence?

How to convert sentence that contains “no more than 3” into predicate logic sentence?

For example: "No more than three $$x$$ satisfy $$R(x)$$" using predicate logic.

This is what I have for "exactly one $$x$$ satisfies $$R(x)$$": $$\exists x(R(x) \land \forall y(R(y) \rightarrow (x = y)))$$

$$\forall x \forall y \forall z \forall u ((R(x)\wedge R(y) \wedge R(z) \wedge R(u)) \rightarrow (x=y \vee x=z \vee x=u \vee y=z \vee y=u \vee z=u))$$
$$\exists x \exists y \exists z \forall u (R(u) \rightarrow (u = x \lor u = y \lor u = z))$$