# Questions tagged [logic-translation]

For translating between natural language expressions and logic expressions.

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### Negating "He will sink unless he swims" [closed]

I want to negate "He will sink unless he swims" using the formula $$\neg (P \Rightarrow Q) \equiv P \wedge (\neg Q).$$ But first, how do we write that statement as if-then statement?
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1 vote
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### Symbolising an following argument with two Therefore's

I am trying to translate the following argument to logic symbols to verify its validity using truth tables: If the supplier supplies the seeds, then if the seeds are sown on time, then the plants ...
1 vote
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### Writing the definition of Upper Bound

Let X be an ordered set. Let $S \subset X.$ An element $u \in X$ is said to be an upper bound for $S$ if $s \leq u$ for all $s \in S.$ In first-order logic, how do I write the above definition? Is ...
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### Choosing between the 'and' and 'implies' connectives

$pol(x): x$ is a politician $liar(x): x$ is a liar All politicians are liars : $\forall x(pol(x) → liar(x))$ Some politicians are liars : $\exists x(pol(x) \land liar(x))$ No politicians are liars :...
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### Do these two logic transaltions have the same meaning?

From Rosen's Discrete Math textbook: Translate the statement “Every real number except zero has a multiplicative inverse.” (A multiplicative inverse of a real number $x$ is a real number $y$ such ...
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### Maximizing Perimeter of Triangle PDE on a Parabola and Finding Coordinates of N for Rhombus Formation

Given a parabola in the Cartesian plane defined by the equation ( $y = -\frac{1}{2}x^2 + \frac{3}{2}x + 2$), it intersects the x-axis at points A and B, and the y-axis at point C. Consider a point P ...
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### Counting the numbers of quantifiers, how are there 4?

From the book "Gentle Introduction to Art of Mathematics": How many quantifiers does this have and what kind? "Everybody has some friend that thinks they know everything about a sport.”...
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### Do ∃x(Dog(x)) and ∃x(¬Dog(x)) contradict each other? [closed]

Formally, ∃x(Dog(x)) and ∃x(¬Dog(x)) look like they contradict each other. However, in the real world, there exist objects which are dogs i.e. ∃x(Dog(x)) there exist objects which are not dogs i.e. ∃...
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### Which of these translates the universal and existential quantifiers better?

Consider this proposition (which I know is false): $$(\exists y{\in}\mathbb Z)\,(\forall x{\in}\mathbb Z)\,(y > x).$$ I am wondering whether the analogy of picking a variable value according to the ...
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### Translating "Boris hasn't tried anything better than chocolate"

Boris hasn't tried anything better than chocolate. The above sentence needs to be converted to first-order logic. The given domain is candies, and Boris is a sentient piece of candy. $B(x,y)$: $x$ is ...
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### Formalising "every number other than $0$ has a unique multiplicative inverse"

The domain is the set of all real numbers. Express "Every number other than 0 has a unique multiplicative inverse" as a logical expression. My solution is: ...
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### "No integers $x$ and $y$ exist for $28x+7y=8$"

What is the logical structure of this statement? No integers $x$ and $y$ exist for $28x+7y=8.$ I'm not sure, but I think the answer is $$¬∃x\;∃y\;(x ∈ \mathbb Z ∧ y ∈ \mathbb Z ∧ 28x + 7y = 8).$$
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### How do I translate "is not sufficient" into symbolic logic?

Take the proposition "it is not sufficient for the monkey to dance in order for me to get an A on the test" m = the monkey dances a = I get an A on the test It makes sense why I can ...
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1 vote
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### "Neither Ana nor Bob can do every exercise but each can do some."

I’m a bit confused as to how I should translate the following sentence: Neither Ana nor Bob can do every exercise but each can do some. I've identified the atomic sentences $A$ = Ana can do every ...
1 vote
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### Expressing the instance of a ZF Set Theory axiom for a given property

I am currently in the process of studying ZF Set Theory (without the Axiom of Choice) and I have come across a type of question that is unclear to me. The basic format of the question is to "...
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### Predicate Logic "John drinks any type of drink"

For the following English statement,what would be the correct predicate logic translation: John drinks any type of drink. 1.$\forall x {(Drinks(John,x))}$ 2.$\forall x(Drink(x) \to Drinks(John,x)\\$ I ...
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1 vote
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### Have I misunderstood this argument about truth values? [closed]

7.2.1 Every truth value is confirmed by intuition that affirms it. $(∀x)(Tx\to Ix)$ 7.2.2. Every intuition that affirms truth value is a feeling of correctness. $(∀x)(Ix\to Cx)$ 7.2.3. The feeling ...
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### Mixing predicate logic with propositional logic

In this paper in legal philosophy (https://doi.org/10.3790/rth.40.1.1) on p. 25, the author writes: P(x) ↔ (x → ¬h) This is supposed to be a formalisation of the following statement: "Every ...
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### Translating English to predicate logic with units

I am having difficulty translating this fragment from a larger sentence into predicate logic: three pets bathe together. Let pets be P(x) and B(x,y) be bathe togehter. How would I deal with the number ...
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