# Tagged Questions

Questions concerning predicate calculus, i.e. the logic of quantifiers.

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### In set builder notation, must the predicate have only one free variable?

question about set theory here, probably quite elementary. When we use the notation $t\in\{x \mid \Phi(x) \}$, whether in an actual set theory or just as an abbreviation for $\Phi (t)$, must it be ...
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### Having an algorithm given a set of axioms and a sentence, can it prove all possible thorems?

Suppose we have an algorithm which, given a set of axioms $A$ and a sentence $P$ can prove if $A \implies P$. Would such algorithm be able to prove any possible theorem implied by these axioms? Is ...
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### Confused by a step in the 'Rule C' proof in Mendelson's Logic Textbook

I've been working through 'Introduction to Mathematical Logic, 5th Ed' by Mendelson, and I've found a step in the proof of proposition 2.10 (Rule C) that I cannot understand. In the proof of this ...
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### Predicate Calculus help

Working on predicate calculus this week, and was hoping I've got these correct, but I'm sure I've made some mistakes for sure.. All programmers enjoy discrete structures not all integers are ...
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### Predicate Logic Statement Requirements

If I want to translate the following sentences to predicate logic: All students enjoy math. is it ok to specify $x$ are students and just do the following? $$M(x) = x \text{ enjoys math}$$ so ...
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### Translate “If any cat is shy, then it is not happy” into predicate logic

Given $C(x)$ is “$x$ is a cat” $S(x)$ is “$x$ is shy” $T(x)$ is “$x$ is happy” translate the following sentence to predicate logic If any cat is shy, then it is not happy. This is what I ...
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### Resolution Algorithms and one Example Problems?

We have a problem in one Resolution question. There is $5$ clauses, and want to prove the $6$th clause is true. which of the following clause is need more than one times to prove $6$th clause? $t$ ...
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### Chartrand Mathematical Proofs 3e Exercise 5.45

I am self-studying this book, and I'm not sure if there is a typo in this question, or there is a gap in my understanding. The question is: Let $R(x)$ be an open sentence over a domain S. Suppose ...
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### CNF Conversion and one $2015$ exam questions?!

if $\text{likes}(x,t)$ means that person $t$ likes food $x$, and $\text{food}(x)$ means $x$ is a food, $\text{CNF}$ of sentence "No food is liked by all person", and $F$ is Skolem function. The ...
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### Negating the statement $\exists x \in \Bbb R$ so that $x$ is not an integer, $x > 2016$, and $\lfloor x^2 \rfloor = \lfloor x \rfloor^2$

There exists a real number $x$ so that $x$ is not an integer, $x > 2016$, and $\lfloor x^2 \rfloor = \lfloor x \rfloor^2$. I would like clarification on how to negate this. My idea of negation is ...
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Consider a signature $\Sigma = \{ P^1, R^1, c\}$. Where $P^1, R^1$ are unary predicates, and $c$ is a constant. Let A be a formula in FOL over $\Sigma$. Prove/Disprove: If A is satisfiable ...
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### Unary relation in a logical sentence

I'd appreciate help with this sentence: Let there be a language L and a structure M, and I need to prove the following sentence is logically false: $$\varphi :\exists xR(x)\rightarrow \forall yR(y)$$ ...
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### True or falsehood of open formula under a fixed interpretation

Given the open formula: $\alpha =(\exists{{x}_{2}})({P}^{1}({x}_{1},{x}_{2}))$ And consider the interpretation $I$ where the domain is the natural numbers, and ${P}^{1}$ means equality. Is $\alpha$ ...
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### Using separators as functional symbols in first order logic

Suppose we have the following definition of a term: A $term$ is: $x$, where "$x$" is a variable $c$, where "$c$" is a constant symbol $f(\tau_1,...,\tau_n)$, where "$f$" is a ...
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### Logic: Who doesn't eat meat, is vegetarian

How to translate "Who doesn't eat meat, is vegetarian" into a formula with predicate letters Lx meaning x is meat, Exy meaning x eats y, and Vx meaning x is vegetarian? I tried, "for every x and for ...
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### Calculating a likely position in 0.5 seconds with only the knowledge of the last second (x,y coordinates)

I have x,y coordinates for football players (22) at a rate of 10 records per second - for an entire football match. I have created an animation of the match with the player locations updates at a ...
Ex: A student must take at least $60$ course hours, or at least $45$ course hours and write a masters thesis, and receive a grade no lower than a B in all required courses, to receive a masters degree....
Ex: A passenger on an airline qualifies as a frequent flier if the passenger flies more than $25,000$ miles in one year or takes more than $25$ flights during that year. I started and made up these ...