I have received a question for my homework and want to see if I'm heading on the right track or not, especially with the use of quantifiers.
Question
Let A be the set of Discrete Mathematics students, B the set of students of Boolean Algebra and S the set of all students. Use rules of inference with quantifiers to formalize the three statements:
P: If someone is a student of Discrete Mathematics, then, they must study Boolean Algebra.
Q: If there exists at least one student of Discrete Mathematics, then, all students of Boolean Algebra study Discrete Mathematics.
R: If all students of Boolean Algebra study Discrete Mathematics then nobody studies Discrete Mathematics.
My not-so-good answers:
P: ∃x A(x) → B(x)
Q: ∃x A(x) → (∀x B(x) → A(x))
R: (∀x B(x) → A(x)) → ∀x¬A(x)
A(x) is the statement 'x is a Discrete Student', B(x) is the statement 'x is a Boolean Algebra Student'.
P: ∀x A(x) → B(x)
Q: ∃x A(x) → (∀x B(x) → A(x))
R: (∀x B(x) → A(x)) → ∀x¬A(x)