Suppose I want to translate the following english statement to first order logic:
Every student loves some student.
What is the difference between these two:
∀x[Student(x) → ∃y[Student(y) ∧ Loves(x,y)]]
∀x∃y Student(x) → (Loves(x,y) ∧ Student(y))
Does the separation of the quantifiers make a difference?