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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    $\begingroup$ 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. $\endgroup$ – 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 $(\text{RightOf}(x,y) \land \text{Large}(x))$

There's no reason the scope cannot have free variables.
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 $\land$?


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