# Questions tagged [logic-translation]

For translating between natural language expressions and logic expressions.

296 questions
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### Propositional Logic Translation from sentence

I'm trying to translate below sentences to propositional logic but I don't know if my understanding of the main steps of translation are correct or not. I would like to ask for help to correct me. ...
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### In Discrete Mathematics, is there a difference between $(\neg P \wedge \neg Q)$ and $\neg (P \wedge Q)$?

I am wondering, in discrete mathematics, whether there is a difference between $(\neg P \wedge \neg Q)$ and $\neg (P \wedge Q)$. My query comes from a practice problem in a book: Either John and ...
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### Language, Proof & Logic (LPL) Exercise 11.21 - Sentences 7, 9

I'm working on LPL's Exercise 11.21, which asks to provide translations of the English language sentences into First Order Logic sentences. Unlike the majority of exercises in the book, as I ...
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### Propositional Logic Translation

I am trying to convert the following into propositional logic in order to construct a semantic tableaux: If Mark goes to the party, then so does Pat. John or Pat will go to the party. John will not ...
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### Predicate Logic Natural Number Problems

I am trying to translate the following statements into predicate logic using the following predicates: $E(x) = x$ is even, $P(x) = x$ is prime, $L(x,y) = x < y$ (i): Some Primes are Odd. (ii): ...
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### Universal Quantified Statement being equivalent when variables are swapped

I was given this statement and asked to express this with universal quantifiers. Likes(x,y) is a Binary Relation that means that person x likes person y. The statement given was: "Everybody is ...
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### How to write “There is at least 2 Cars are not the same Colour” in logic

I would like to know how to write “At least 2 Cars are not the same Colour” in logic. I know that "at least two cars" can be defined as ∃x(C(x)∧∃y(C(x)∧y≠x)). is ...
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### how to convert sentence that contains “no more than 3” into predicate logic sentence?

How to convert sentence that contains “no more than 3” into predicate logic sentence? For example: "No more than three $x$ satisfy $R(x)$" using predicate logic. This is what I have for "exactly ...
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### Why is my translation of $\exists{x}\,(C(x) \rightarrow F(x))$ into an English sentence wrong?

Let $\text{C(x): x is a comedian}$ and $\text{F(x): x is funny}$ Let $$\alpha:\quad\exists{x}\,(C(x) \rightarrow F(x))$$ and the domain consists of all people. I needed to translate $\alpha$ into ...
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### Logic Translation

"a and e are both larger than c, but neither is large" I thought the translation $$\large (\text{Larger}(a, c)\land \text{Larger}(e, c))\land\lnot(\text{Large}(a)\land \text{Large}(e))$$ would be ...
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### First Order Predicate Logic

I would like some help to check my solution for the translation of a sentence into predicate logic. The sentence is given as: ...
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### Translating Predicate Logic to English

$E(x,y)$: $x$ can eat $y$ $L(x,y)$: $x$ loves eating $y$ $D$ is the domain of all dogs $S$ is the domain of all snakes Predicate Logic to English:             &...
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### Translating english sentences to predicate logic

Trying to practice translating english sentences into predicate logic and vice versa. $E(x,y)$: $x$ can eat $y$ $L(x,y)$: $x$ loves eating $y$ $D$ is the domain of all dogs $S$ is the domain of all ...
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### Translating into Logical Statements

I was giving the following sentence to translate into a logical statement. “Everyone has exactly one best friend" The way I set it up is by letting ...
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### is this predicate logic statement correct for this indirect proof?

Just for context, my goal is to prove the square root of 2 is an irrational number. I already did this using proof by contradiction both algebraically and geometrically, however, I want to begin the ...
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### “Although it is necessary for $n$ to be prime in order for $R_n$ to be prime” as logic statement

This is a statement about Repunits from this paper. How can I write this as an if/then statement? Knowledge about Repunits isn't required. The question is basically: what does "although it is ...
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### Confusion in determining an argument's validity?

I understand that an argument is basically an implication in the sense that: $$premise1 \land premise2 \land premise3.... \to conclusion$$ And an argument would be considered valid when such an ...
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### logical equivalence in predicate logic

I was studying discrete mathematics, one of the basic subjects in cs department. In particular, studying the chapter "Logics", I came to have some trouble. While solving problem saying " Let $S(x)$ ...
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### Negating first order logic

I am struggling to understand how to really negate in first order logic. Take the following examples: "Somebody loves everybody" Negating this would be: "It is not the case that somebody loves ...
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### Rewrite each of the following sentences using logical connectives

Rewrite each of the following sentences using logical connectives. Assume that each symbol $f, x_0, n, x, S, B$ represents some fixed object. (a) If $f$ has a relative minimum at $x_0$ and if $f$ ...
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### Predicate Is Before The Subject Is This The Correct Translation?

I'm trying to figure out what the proper translation in predicate logic would be for the example below, I'm confused because the predicate comes before the subject. So i'm wondering if I need to ...
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### “Except” in predicate logic

I have a phrase that I am trying to translate into predicate logic. The phrase is as follows: All lions except old ones roar So far I have written down that: $∀x((L(x) \land \lnot O(x)) \to R(x))$...
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### Is the negation of “p iff q”, “(not p) iff q”?

My logic teacher says that the negation of $p \!\!\iff\!\! q$ is $(\lnot p) \!\!\iff\!\! q$. This seems wrong to me, because I feel like $(\lnot p) \!\iff\! q$ is a too strong statement to be the ...
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### truth value of “if…then…”

From the truth table, when both $p$ and $q$ are true, then "if $p$ then $q$" is true. However, this is a little weird as "if $p$ then $q$" is used to show the relationship between $p$ and $q$. If $q$ ...
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### Predicate Statements— Every person loves at most only one reindeer

I was given a question by my professor during lecture today, to translate into predicate logic statements, "Every human loves a reindeer, but every human loves at most only 1 reindeer", without ...
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### Confused with regard to converting English sentences to If-Then Conditional Logic

Whenever I come across questions, where they ask me to translate English sentences to propositional logic, I often have trouble figuring out which is the if and which part of the sentence is the Then....
Suppose I want to express this sentence in first-order logic: "Many printers are broken" If $p(x)$ is true if the term $x$ is a printer and $b(x)$ is true if $x$...
What is the proper way to write this statement mathematically? "All people are smokers or non-smokers but not both." $H = humans, S = smoker, NS = non-smoker$ My first attempt was: \forall x \...