I have a small problem with the first order logic, in particular, predicate logic
Let us take this sentence as an example:
Each teacher has given a form to each student.
From this sentence, can we have different reading?
This is my try to solve such problem, I did not know if this is the answer for such question:
Every Teacher has given a form to each Student.
(∀x)Teacher(x)^(∀y) Student(y)^(∃z)Form(z)^Give(x,y,z)
If X is a Student then he has received a form from a teacher
Student(x)→(∃y) Teacher(y)^(∃z)Form(z)^Give(x,y,z)
If X is a Teacher then he has gave a from for all his students
Teacher(x)→(∀y) Student(y)^(∃z)Form(z)^Give(x,y,z)
If X is a form then a teacher gave it to all student.
Form(x)→(∀y) Employer(y)^(∃z)Teacher(z)^Give(x,y,z)
EDIT
To clarify my needs !
I think that the form is in logical dependency, either of student, either of teacher, or both, so we can find three other readings; so What are those reading? (Look at the begining to find what I did)
And How can I transform this sentence in predicate logic?
Each teacher has given a form to each student.
because it seems that
(∀x)Teacher(x)^(∀y) Student(y)^(∃z)Form(z)^Give(x,y,z)
is wrong.