Please check my predicate logic answer

Question

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)

I think you need to review quantifiers. – Adrian Keister Jan 03 '20 at 22:10 — Adrian Keister, Jan 03 '20 at 22:10

score 1 · Answer 1 · answered Jan 03 '20 at 22:14

1

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))] $

answered Jan 03 '20 at 22:14

Adrian Keister

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Thanks, i definately tripped up on the quantifiers. Do the brackets make much difference? – prinve228 Jan 03 '20 at 22:31
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Not really. Some authors always use them, some don't. If clarity suffers from the lack, then USE THEM. – Adrian Keister Jan 03 '20 at 22:56

Please check my predicate logic answer

1 Answers1