1. A

    Which solution is better for this predicate?

    We have this predicate: Now I have to turn this in English. I come up with three answers: 1) x is a prime number if x is greater than 1, and if for every given y that is divisible by x, then y is either 1 or x itself. 2) x is a prime number if x is greater than 1, and for every given...
  2. J

    How to rewrite these formulas in the opposite form?

    I want to know how I can write from some predicate formula its negative form. For example ∀x∃y(x R y) then not(∀x∃y(x R y)) is equal to ∃x,not ∃y(x R y)))(not exist y) How do these formula work with conjunction implication and disjunction? Bellow are examples of some formulas but...
  3. L

    Predicate Logic Help

    I need help with these 3 questions on Predicate Logic Proofs... I'm beyond lost at the moment. Here's a link for a picture of the questions. Predicate Logic - Album on Imgur
  4. S

    Am I doing this right? (Predicate logic)

    Hey thanks for checking the thread! So i have to prove a conclusion is true with predicate logic I don't have a step by step solution so i tried myself That's my problem : Conclusion : ∃x : ¬Q(x) Premises : 1.∀ : x (P(x) → ∀y : (Q(x) → R(x,y))) 2 ∃x : (P(x) ∧ ∃y ...
  5. E

    Need some tutorial with predicate logic in Label Transition system

    I picked up this module a week ago but they assume people have background about predicate logic and mathematical proof skills, sadly, I don't. So here I am, really need someone explain to me how to interpret this kind of question and the notations in the question thoroughly. Here comes the...
  6. P

    Predicate Logic Problem

    Hello, I am having particular trouble with the below problem. We are using Tourlakis' Logic Textbook and we must prove this statement using Hilbert style or Equational style proof (first-order logic), but any proof of any type would point me in the right direction. (∀x)(A→B) ≡...
  7. E

    Simplification Normal Form - predicate logic

    Hi! Can you please help me solve this question? (p → (q Λ r V s)) → ((p → q) V (r V s)) Convert into Disjunctive Normal Form(DNF) and Conjunctive Normal Form(CNF). Thank you in advance.. :)
  8. J

    Implicative definitions in predicate logic

    Hello, I am supposed to complete next exercise soon. This is my solution: true all x. all y. all z. (Left(x,z,y) -> Reach(z,y)). true all x. all y. all z. (Right(x,z,y) -> Reach(z,y)). true all x. all y. all z. (Up(x,z,y) -> Reach(x,z)). true all x. all y. all z. (Down(x,z,y) ->...
  9. K

    proof using Predicate Calculus

    Hello, I've started my proof for the following sequent, any assistant/comments will be appreciated prove: (∀x)(∀y)(∃z) (R(x,z) ∧ R(y,z)) ⊢ (∀x)(∃y) R(x,y) 1 (1) (∀x)(∀y)(∃z) (R(x,z) ∧ R(y,z)) A 1 (2) (∀y)(∃z) (R(a,z) ∧ R(y,z)) 1 ∀E...
  10. S

    predicate logic

    translate the following sentences: (i) Mary has a false passport. F(m,p) (F=False, m=Mary, p=Passport) (ii) Peter likes nobody but himself. (iii) Mary only dates Americans. (iv) Smoking is dangerous. D(s) (D=dangerous, s=Smoking) (v) Not everybody cooked their own dinner. ¬?x (C(x)...
  11. S

    Predicate logic - true or false formulae

    Hello everyone, I can't seem to understand how to do this question. Determine whether the formula F: ?x?y(P(x) ? x = y) is true or false under each of the following interpretations over the domain D = {a, b}. (i) both P(a) and P(b) are true; (ii) both P(a) and P(b) are false; (iii) P(a) is...
  12. M

    Predicate Logic

    I am new to this topic. Can someone please be kind enough to: Construct a Predicate Logic proof for the following statement: "No athletes are bookworms. Carol is a bookworm. Therefore Carol is not an athlete" Thank you!!!
  13. D

    Finding a domain and predicate

    Here I am again, trying to figure out these confusing things... sorry I need to define a domain U and predicate P for which this condition evaluates as false... [? x ? U, P (x)] ? [? x ? U, P (x)]. What's the correct way of finding them? How can this expression be possible anyways? Unless x...
  14. D

    Help with predicate form

    Hi all, I am currently studying for an exam and need help working out predicate forms. The first one is easy {3,6,9,12,15} would be {x E N: x<=15 and x is a multiple of 3} However how to express the following is giving me a headache. {...-12, -8, -4, 0, 4, 8, 12...} {1, 0.5...
  15. P

    Predicate Logic

    Hi all, I answered the following question. Can anybody Confirm my answer... Question is As follows.. Q1. A certain cabal within the 6.042 course staff is plotting to make the final exam ridiculously hard. (“Problem 1. Prove that the axioms of mathematics are complete and consistent. Express...
  16. P

    Translate sentences from English to predicate

    Hi all, I'm a Software Engineer. I'm currently taking some online free courses in "Mathematics for Computer Science". I stumbled across this question but couldn't able to answer it. Please help to answer the question Translate the following sentences from English to predicate logic. The domain...
  17. F

    predicate quantifiers

    I'm trying to understand meaning of quantifiers for a predicate Let's say I have the following statement: Every American has a dream. Let A be the set of Americans, let D be the set of dreams, and de?ne the predicate H(a, d) to be “American a has dream d.” Let's say I want to write the...
  18. L

    Predicate calculus

    In the universe of discourse U2 = Pf (Z+), Prove or disprove each of the following statements: (a) (?X)(?Y ) X ? Y = Y ? X = Y . (b) (?Y )(?X) X ? Y = Y ? X = Y . (c) (?X)(?Y ) X ? Y = Y ? X = Y . (d) (?Y )(?X) X ? Y = Y ? X = Y . I am unable to do this question! any help would be much appreciated
  19. O

    proof in predicate calculus

    Let : 1)P one place operation ............................................m is a constant........................... 2)K one place operation let : 1) G two place predicate 2) H two place predicate Let : The following axioms or assumptions) 1)for all A { H(A,m)v H(m,A)v G(A,m)} 2)for...
  20. W

    Decidable subclasses of first order predicate logic

    Hi, I apologize for my English:). I am doing thesis which is called: decidable subclasses (subsets) of first order predicate logic, but I cant find on this topic no proper information. Do you have someone available summary of these subclasses? or any material? Thank you very much!