Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [logic-translation]

For translating between natural language expressions and logic expressions.

3
votes
2answers
49 views

Express Negation in Simple English: There is a student in this class who has chatted with exactly one other student

Am I correct in the following: If the domain is all students, and C(x,y) is the predicate of x having chatted with y. Then the sentence There is a student in this class who has chatted with ...
0
votes
2answers
29 views

Translate a sentence into predicate logic

I want to translate this sentence There exists $a$ such that if for all $b$ different from $a$, $b$ has the propriety $P$ then $a$ has the propriety $Q$ I translated it like this : $\exists a. ...
0
votes
3answers
55 views

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 ...
2
votes
1answer
35 views

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 ...
0
votes
1answer
36 views

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): ...
0
votes
1answer
25 views

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 ...
0
votes
1answer
49 views

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 ...
0
votes
1answer
35 views

Predicate Calculus and Statement

I'm having a hard time to understand predicate Calculus, Statement and Prolog programming. Let $male$ be a unary predicate symbol with the indicated meaning. Let $parent$, $son$, $sibling$, and $...
1
vote
3answers
34 views

Rewriting a logical statement

Only lakers are irrational people. I believe it technically should be translated as: All irrational people are lakers. Is there is any way at all to rewrite the above statement to mean the ...
2
votes
1answer
46 views

Rewriting predicate sentences to logically equivalent statements that doesn't use the negation operator

a) $\sim\! \exists x \in \mathbb{H}_{\sqrt{2}}, \forall n \in N, \sim\! \exists z \in \mathbb{R}, (x^n > z) \land \sim\! (z < n)$ b) $\exists x \in D, \sim\! \forall y \in C, \sim\! \exists n \...
0
votes
2answers
76 views

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 ...
0
votes
0answers
36 views

Translating predicate logic statements to english [duplicate]

Consider the following predicates over the domains $B$ of all bunny rabbits, $M$ of all magicians, and $J$ of all jazz musicians. $F(x; y)$: person $x$ sent a friend request to person $y$. $D(x; y): ...
4
votes
1answer
46 views

Translating predicate logic statements

Consider the following predicates over the domains $B$ of all bunny rabbits, $M$ of all magicians, and $J$ of all jazz musicians. $F(x; y)$: person $x$ sent a friend request to person $y$. $D(x; y): ...
4
votes
2answers
51 views

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 ...
1
vote
1answer
49 views

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: ...
1
vote
2answers
60 views

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:             &...
0
votes
1answer
53 views

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 ...
0
votes
1answer
20 views

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 ...
0
votes
1answer
24 views

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 ...
1
vote
2answers
65 views

“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 ...
2
votes
1answer
43 views

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 ...
0
votes
1answer
34 views

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 $S(x)$ ...
1
vote
2answers
64 views

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 ...
2
votes
1answer
88 views

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 $f$ ...
3
votes
2answers
41 views

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 ...
2
votes
2answers
218 views

“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: $∀x((L(x) \land \lnot O(x)) \to R(x))$...
0
votes
6answers
240 views

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 ...
3
votes
4answers
109 views

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 $q$ ...
1
vote
2answers
137 views

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 ...
0
votes
2answers
61 views

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....
-2
votes
1answer
38 views

“Many” quantifier in first order logic [closed]

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 $x$...
1
vote
1answer
30 views

Properly Translate Propositional Statement to Discrete Math

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 \...
0
votes
2answers
30 views

Expressing interrelationships in first order logic

I'm trying to figure out how to best formalize the following interrelationship in first order logic: A material has (electric) resistance $r$ and conductance $g$, and the two are related as $r \...
3
votes
3answers
184 views

When “If $A$ is true then $B$ is true”, is it valid to assert that “If $B$ is false, $A$ must also be false”?

If it is given that: "People that ride buses, also ride planes" then is the statement "people that don't ride planes, also don't ride buses" necessarily true? I don't think so, but the ...
0
votes
3answers
171 views

Probability problem with or/and (meaning of “neither”). [closed]

In a certain Algebra 2 class of 28 students, 5 of them play basketball and 21 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly ...
3
votes
1answer
94 views

“There is only” in first order logic

I'm trying to translate the statement "There is only three things that are not small" into first order logic. I'm using some software to verify my sentences, but I feel like I don't understand what "...
0
votes
1answer
44 views

How this statement should be written?

If I have a theorem/conjecture of the form "Let $n$ be an [object with some properties], then $P(n)$", how would it be written in logic ? So I have 2 variants: 1)$\forall n \in A, P(n)$. 2)$(n\in A)\...
1
vote
1answer
62 views

Logical Formalization of: “Children don't eat pasta with spinach or mushrooms on it”

I want to formalize the following sentence in predicate logic: If a children has spinach or mushrooms on its pasta then it will not eat its pasta. The headline contains a shorter version. I have ...
1
vote
1answer
90 views

All students in a class are friends with some students in all engineering faculty

All students in a class are friends with some students in all engineering faculty. My solution was Domain $x,y$ is a student Domain $z$ is engineering faculty $M(x)$ students in this class $S(x,y)$; ...
1
vote
0answers
34 views

Are these formalization in predicate logic correct?

The sentence I want to formalize is the following: Every Italian likes to eat pizza. I come up with the following solutions: $$\forall x \forall y(Italian(x) \land Pizza(y) \implies LikeToEat(x,y)...
2
votes
2answers
23 views

What is the difference in meaning between these two antecedents …?

$$ (\forall x)(Mx \to Wx) \to \quad... \tag{1} $$ $$ (\forall x)(Mx \land Wx) \to \quad... \tag{2} $$ The consequent is clear: $\, (\exists y)(Fy \land Sy)$ The statement is: If every member of ...
0
votes
2answers
48 views

Verification of the translation of English sentences into predicate logic.

I want to translate some sentences into predicate logic [based off the text "Language, Proof and Logic" (Barwise, Etchemendy) 1st ed]. The sentences are as follows: Only in front of large objects is ...
2
votes
2answers
135 views

How to convert … to logical symbols?

If Bluenose is guilty then no witness is lying unless he is fearful. There is a witness who is fearful. Therefore, Bluenose is not guilty. $$B\to[(\forall x)(\,(Wx\land\lnot Fx)\to(\lnot Lx)\,)] \...
0
votes
2answers
87 views

Logical Reasoning Puzzle

Consider there are two tribes living on the Island: Knights and knaves. Knights always tell truth while Knaves always tell lie. Let we encounter two random people A and B, upon asking a question to ‘A’...
0
votes
0answers
47 views

How do I formalize such sentences in predicate logic?

How do I formalize such sentences in predicate logic? ...
6
votes
1answer
47 views

Writing a statement using logical connectives and determining whether it is a logical implication.

I need to write the following statements into logical form and determine whether the conclusion is logically implied by the assumptions. A sufficient condition of $f$ to be integrable is that $g$ ...
1
vote
2answers
278 views

Logic & Negation

(A) Consider the statement $\forall x \exists y \lnot P(x, y)$. Write down a negation of the statement that does not use the symbol $\lnot$. I just said that its $\forall x \exists y P(x, y)$ but I'm ...
0
votes
3answers
46 views

Positively confused about negation

At first, negation was obvious. However, the more I thought about it, the more I got confused on why the answers are what they are. For example, $$P = \text{The real number } r \text{ is at most } \...
1
vote
1answer
42 views

Conversion of English statement to Logic Expression Using quantifiers

I was solving below question from Kenneth Rosen and I had a doubt in it. Let $M(x,y)$ be "$x$ has sent $y$ an e-mail message" and $T(x,y)$ be "$x$ has telephoned $y$", where the domain consists of all ...
5
votes
4answers
1k views

Anyone who knows anything is envied by someone

Anyone who knows anything is envied by someone. Let $K (x,y) = x \text{ knows } y$ $E (x,y) = x \text{ is envied by } y$ I feel like anyone who knows "anything" is supposed to refer to anyone who ...