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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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 ...
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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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On the tautology $(P \implies Q) \vee (Q \implies P)$
The logical statement
$$(P \implies Q) \vee (Q \implies P)$$
is an example of a tautology. However, if I choose logical statements for $P$ and $Q$, it is not always true that either $Q \implies P$ or $...
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When to use implication arrow versus equivalence arrow?
In my class we've been asked to complete an exercise and choose whether to use implication or equivalence arrows: "The equation $2x−4=2$ is fulfilled only when $x=3$."
I understand that we ...
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Finding the relationship (equivalence or implication) between two expressions
I am trying to find the relationship between $$\exists X \; (p(X) ∧ q(X))$$ and $$\exists X \; p(X) ∧ \forall X \; q(X).$$
I believe that quantifiers cannot be used in forming truth tables, after all ...
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Two arguments with the same form, one valid, one not
A convertible car is fun to drive. Isaac’s car is not a convertible. Therefore, Isaac’s car is not fun to drive.
Letting $C(x)$ be "$x$ is a convertible car" and $F(x)$ as "$x$ is fun ...
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Is "William only eats icecream when the sun is shining" a biimplication?
William only eats icecream when the sun is shining
Let $P(t)$ be the sun is shining at time $t.$
Let $Q(t)$ be William is eating an icecream at time $t.$
Which implication is there between $P(t)$ and $...
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Using quantifiers to rewrite some simple mathematical statements
Have I used quantifiers correctly to rewrite these sentences?
The equation $x^3=7$ has at least one root.
$∃x∈\mathbb R\;\;x^3-7=0$
The equation $x^2-2x-5=0$ has no rational roots.
non$(∀x∈\mathbb ...
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Translating "there is no number between two consecutive numbers"
There is no number number strictly between two consecutive number.
Is my translation $$∀x ∈ Z | ∀y ∈ Z | ¬∃z ∈ Z \;(z<y ∧ z>x ∧ y=x+1)$$ correct?
Is $$∃x | ¬∃n ∈ Z \;(n<x<n+1) $$ also ...
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