Let's try to translate the English sentence:
"Everything to the left of every tetrahedron is also to the left of every dodecahedron"
Consider the predicates
Tet(x): x is a tetrahedron
LeftOf(x,y): x is to the left of y
Dodec(x): x is a dodecahedron
Consider the following attempt at a translation:
Apparently this is not an acceptable translation.
A justification for it not being acceptable is that "we should pay close attention to the placement of the ∀y quantifier and note that ∀x (P ⟶ Q) is not equivalent to ∀x P ⟶ Q."
What is wrong with this translation? Is there an alternative explanation than the hint above?
Does the quantifer ∀y in the sentence ∀x ∀y (Tet(y) ⟶ LeftOf(x,y)) mean that "for every object y, if y is a tetrahedron, then for every object x, and for every object y, x is to the left of y"? Are the two occurrences of "for every object y" referring to different objects in this case?
By the way, the following two are apparently correct translations: