Rewriting English statement using quantifiers and predicates

Question

I'm supposed to rewrite the following english statements using predicates and quantifiers:

1. If an object is black, then it is a square.
2. If an object is a square, then it is above all the gray objects.
3. If an object is above all the gray objects, then it is above all the triangles.
4. If an object is above all the triangles, then it is above all the blue objects.

Here's my answer:

Let $O$ be the set of all objects

1. $\forall x \in O$ $($Black$(x)\to$ Square($x))$

2. $\forall x \in O$ $[$Square$(x)\to$ $(\forall y \in O($Above$(x$,Grey$(y))))]$

and so on.

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My question is, for the second statement, is that way of writing ok? Or would something like

$\forall x \in O$ $[$Square$(x)\to$ $(\forall y \in O$ $($Grey$(y)$ $\to$ Above$(x,y)))]$

be clearer?

Answer 1

I think the last one would be a bit clearer.

The reason is: By the rules of predicate logic, you cannot insert a predicate into a predicate, unless you have defined $\text{Above}(x,\text{Grey}(y))$ as an abbreviation of $(\text{Grey}(y) \rightarrow \text{Above}(x,y))$. For example: $(\forall x \in O) P(x)$ is just an abbreviation for $\forall x( x \in O \rightarrow P(x))$.