In trying to understand some predicate calculus notes, let the domain for $x,y$ be buildings, and the domain for $z$ be cities.
Let $H(x,y)$ signify that $x$ is higher than $y$
Let $O(x,y)$ stand for $x$ and $y$ are not the same building
Let $L(x,z)$ stand for $x$ is in $z$,
Then my prof states:
"A building is higher than every other building only if this building is in Toronto"
He writes: this can be formulated as:
$1) \forall x (\forall y(O(x,y) \implies H(x,y)) \implies L(x, "Toronto"))$,
But it cannot be formulated as:
$2) \forall x \forall y ((O(x,y) \implies H(x,y)) \implies L(x, "Toronto"))$
In trying to understand this, I am trying to come up with an example where $1$, $2$ have different truth values for the same $x,y$ values since I believe this is the strategy to show that they are not logically equivalent, but I am stumped and need a hint to continue.