Consider the statement, "There is a building on the campus of some college in the United States in which every room is painted white." Express the statement using quantifiers. Be sure to define your predicate function and specify the domain of each of the three variables. Express the negation of the above logical quantified statement so that no negation is to the left of a quantifier. Write the negation of the statement in plain English.

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"

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line 5 is one of them idk the other one