I have this following natural language statement:
"There is only one house in area1 the size of which is less than 200m²."
which is mistranslated to FOL:
∃x.(house(x) ∧ In(x,area1) ∧ ∀y.(house(y) ∧ In(y,area1) ∧ size(y) < 200 -> x=y))
This translation is wrong according to my lecturer, because it is not necessary that the size of x must be less than 200. The statement is true if there only houses which are bigger.
I have two questions:
I don't get the FOL translation at all and don't see where the uniqueness part is expressed : so translated it back : "if all houses in area1 have a size less then 200m² then there exists one house which equals to all houses ??"
why is not necessary that the size of x is less than 200, when it clearly says in the statement above that must exist one house with a size less then 200 ?