Scope of quantifier

I had a question about how to write the scope of a quantifier. I know that the scope should not have any free variables in it, but then how would be write the scope of the second quantifier($$\exists y$$) in the sentence $$\forall x\exists y(\text{RightOf}(x,y) \land \text{Large}(x))$$

I thought maybe we just write the sentence with the first quantifier($$\forall x$$) in it, so my answer looked like this $$\forall x(\text{RightOf}(x,y) \land \text{Large}(x)).$$

However, this was incorrect, so I was wondering if anybody knew how we would write the scope?

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• The scope will have free variables, as a formula: after all, you've taken away a quantification, so the variables previously quantified will end up free. – Simone Ramello Aug 14 at 8:49

The scope of $$\forall x$$ is $$\exists y(\text{RightOf}(x,y) \land \text{Large}(x))$$
The scope of $$\exists y$$ is $$(\text{RightOf}(x,y) \land \text{Large}(x))$$
That formula is equivalent to $$\forall x\exists y \text{RightOf}(x,y) \land \forall x\text{Large}(x)$$
What now is the scope of $$\land$$?