So I have a few questions about determining which formula it is:So if a binary predicate symbol $X$ denotes an edge between two variables, say $x$ and $y$, for the following formulasWhy is $\forall x \exists y\,(X[xy]\lor X[yx])$ universal and $\exists x \forall y\,(X[xy]\lor X[yx])$ existential? I mean for the second formula all $y$ are within the scope of $\forall y$, so shouldn't it be universal as well?And if you have a formula like this: $(\exists x X[xy]) \odot X[yx]$, where $\odot$ denotes an arbitrary binary connective, would this be a binary connective formula or an existential formula?Thanks.
When is a first-order formula is existential and when is it universal?
logic;first order logic