Answer
The mathematical Expression of the given expression is
$\exists z \exists y \forall x P(x, y, z)$
Work Step by Step
Let us consider:
P(x, y, z) = “Room x of building y of college z is painted white”
Domain x: all rooms
Domain y: all buildings of a campus
Domain z: all college in the United States
We can note form the expression that “there is a building on the campus of some college in the United States in which every room is painted white.”
The room depends on the college and building, while the building depends upon the college.
Using the above interpretations, we can then rewrite the statement as the mathematical expression:
$\exists z \exists y \forall x P(x, y, z)$
