Answers.Body: <p>Your two trials are obviously wrong since the occurrence of the latter <span class="math-container">$x$</span> are both free if you pay attention to its scope and paranthesis, and your last trial cannot be salvaged since such student may possibly learn non-IT subjects too. You can salvage your first trial as <span class="math-container">$∃x (student(x) \land ∀y(ITsubject(y) \to learn(x, y)))$</span>, which could be further converted to prenex normal form <span class="math-container">$∃x∀y (student(x) \land (ITsubject(y) \to learn(x, y)))$</span> or <span class="math-container">$∃x∀y (student(x) \land (\lnot ITsubject(y) \lor learn(x, y)))$</span>. And from this it shows your teacher's translation is incorrect or there's some typo in between, which is also apparent semantically since your teacher's version means every subject in your universe is ITsubject which is trivial here and most likely false in most 1-sorted context.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-11-27T02:39:48.240Z
Answers.Text: sorry i forgot the parenthesis, and you say the statement of my teacher is trivial so that its neither false nor true in some case?
Answers.UserDisplayName: chews
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Answers.Text: It should be $∃x∀y(student(x)∧(¬ITsubject(y)∨learn(x,y)))$ as shown in the end of my above answer which is obviously not logically equivalent to your teacher's version or entail it (unless you can show how to derive from mine to your teacher's version). Also semantically your teacher's version is wrong translation per common sense, and by "trivial" here I mean your teacher's version is false unless your FOL is *2-sorted* and in the universe for $y$ there're only ITsubject(s), nothing else, which is trivial per common sense.
Answers.UserDisplayName: cinch
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Answers.CreationDate: 2022-11-27T06:41:43.387Z
Answers.Text: Also u say the last trial not salvaged but like this sentences: There is an agent who sells policies only to people who are not insured.Translation : (∃x )(Agent(x) ∧ ( ∀ y) SellsPolicy(x,y) => ~Insured(y)) why this wouldnt be (∃x )(Agent(x) ∧ ( ∀ y) ~Insured(y) => SellsPolicy(x,y)) why don't they invert the SellsPolicy(x,y)) after the =>
Answers.UserDisplayName: chews
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Answers.UserDisplayName: cinch
Body: <p>I have the following sentence, which I need to write in FOL</p>
  <blockquote>
  <p>There exists a student studying all the subjects of the information technology subject</p>
  </blockquote>
  <p>I don't know how <span class="math-container">$\forall$</span> can be combined with the <span class="math-container">$\land$</span>.</p>
  <p>It was written by my teacher as follows</p>
  <p><span class="math-container">$$\exists x, \forall y: \text{student}(x) \land \text{learn}(x, y) \land \text{ITsubject}(y)$$</span></p>
  <p>However, I was thinking this sentence should be written like this:</p>
  <p><span class="math-container">$$\exists x \text{student}(x) \land \forall y(\text{ITsubject}(y) \rightarrow \text{learn}(x, y))$$</span></p>
  <p>or maybe</p>
  <p><span class="math-container">$$\exists x \text{student}(x) \land \forall y(\text{learn}(x, y) \rightarrow \text{ITsubject}(y))$$</span></p>
  <p>Is this right?</p>
  
Tags: <logic><knowledge-representation><knowledge-based-systems>
Title: Are my attempts to write "There exists a student studying all the subjects of the information technology subject" in FOL correct?
UserDisplayName: chews
ThreadText: # Are my attempts to write "There exists a student studying all the subjects of the information technology subject" in FOL correct?
  
  (Asked by: username_0 on 2022-11-26)
  
  I have the following sentence, which I need to write in FOL
  
  > There exists a student studying all the subjects of the information technology subject
  
  I don't know how $\forall$ can be combined with the $\land$.
  
  It was written by my teacher as follows
  
  $$\exists x, \forall y: \text{student}(x) \land \text{learn}(x, y) \land \text{ITsubject}(y)$$
  
  However, I was thinking this sentence should be written like this:
  
  $$\exists x \text{student}(x) \land \forall y(\text{ITsubject}(y) \rightarrow \text{learn}(x, y))$$
  
  or maybe
  
  $$\exists x \text{student}(x) \land \forall y(\text{learn}(x, y) \rightarrow \text{ITsubject}(y))$$
  
  Is this right?
  
  **Tags:** logic, knowledge-representation, knowledge-based-systems
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2022-11-26. Score: 0 | Accepted answer
  
  Your two trials are obviously wrong since the occurrence of the latter $x$ are both free if you pay attention to its scope and paranthesis, and your last trial cannot be salvaged since such student may possibly learn non-IT subjects too. You can salvage your first trial as $∃x (student(x) \land ∀y(ITsubject(y) \to learn(x, y)))$, which could be further converted to prenex normal form $∃x∀y (student(x) \land (ITsubject(y) \to learn(x, y)))$ or $∃x∀y (student(x) \land (\lnot ITsubject(y) \lor learn(x, y)))$. And from this it shows your teacher's translation is incorrect or there's some typo in between, which is also apparent semantically since your teacher's version means every subject in your universe is ITsubject which is trivial here and most likely false in most 1-sorted context.
  
  > **Comments:**
  > **username_0**: sorry i forgot the parenthesis, and you say the statement of my teacher is trivial so that its neither false nor true in some case?  
  > **username_1**: It should be $∃x∀y(student(x)∧(¬ITsubject(y)∨learn(x,y)))$ as shown in the end of my above answer which is obviously not logically equivalent to your teacher's version or entail it (unless you can show how to derive from mine to your teacher's version). Also semantically your teacher's version is wrong translation per common sense, and by "trivial" here I mean your teacher's version is false unless your FOL is *2-sorted* and in the universe for $y$ there're only ITsubject(s), nothing else, which is trivial per common sense.  
  > **username_0**: Also u say the last trial not salvaged but like this sentences: There is an agent who sells policies only to people who are not insured.Translation : (∃x )(Agent(x) ∧ ( ∀ y) SellsPolicy(x,y) => ~Insured(y)) why this wouldnt be (∃x )(Agent(x) ∧ ( ∀ y) ~Insured(y) => SellsPolicy(x,y)) why don't they invert the SellsPolicy(x,y)) after the =>  
  
  ---
  
  