I have a been working on a predicate logic question and wondered if someone could check my answer and possibly point me in the correct direction should it be wrong.
question: Let A be the set of DM students, B the set of BA students and S all students. Formalise the following.
P: If someone is a student of DM, then they must study BA.
my answer: ∃x A(x)-> B(x)
Q: If there exists atleast one student of DM, then all students of BA study DM
my answer; ∃x ∈ A(x)-> (B(x) and A(x))
R: If all students of BA study DM then none studies DM
my answer; ∀x (B(x) and A(x)) -> ∀x A(x)
Here's what I would write:
P: $(\forall\,x)(A(x)\to B(x)) $
Q: $(\exists\,x\in A(x))\to [(\forall\,x)(B(x)\to A(x))]$
R: $[(\forall\,x)(B(x)\to A(x))]\to[\neg(\exists x)(A(x))] $