Answer:
P (x,y,z) = x on the campus of y in the United States in which z is painted white.
Expressed using Quantifier = ∃(x)∃(y)∀(z)P(x,y,z).
Negation =∀(x)∀(y)∃(z)¬P(x,y,z)
Negation statement in English: In all Buildings on the Campus of Every College in the United States, there exist some rooms which are not painted white.
Explanation:
variables = x,y,z
Domain for x is all buildings
Domain for y is all colleges
Domain for z is all rooms
Universal Quantifier ∀ - For all elements , example"every room"
Existential Quantifier ∃ - There exists an element, example "There is a building", "of some college"
The negation will be the opposite quantifier, therefore a universal now becomes existential and therefore changes the Predicate "is painted white" to "are not painted white"
