# Tagged Questions

1answer
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### Solving a version of the liar paradox

Given two people $Alice ,Bob$ are either lying or telling the truth Now suppose $Alice$ says "At least one of us is lying." We have two cases: $Alice$ is telling the truth $\implies$ $Bob$ is ...
1answer
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### Tranlsation of english to nested quantifiers and forming their negations

You are given the following propositional function: B(x,y): Writer x has written a book on subject y. The domain for x is all people in the world, and the domain for y is all subjects in the world. ...
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### Island of knights and knaves

This question is about an island of knights and knaves, where knights always speak the truth and knaves always lie. You encounter two people A and B. Determine, if possible, what each of them are if ...
2answers
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### Quantified Logic with miltuple variables

Problem: ∀y¬∃x¬(¬Fxy ∨ Fyx) ⊢ ∀y∀z(Fyz→Fzy) I don't really understand how to deal with multiple variables in instances like this. So far I have: ...
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### 3-Coloring a graph using propositional formulas

Hello everyone I am studying for an exam on logic and computability, I am trying to tackle a specific problem so any help would be greatly appreciated: Let $G = (V,E)$ be an undirected graph ...
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### Validity of three syllogisms with venn diagram

me and my study group are struggling with a "how to proof syllogism conclusions" approach. We got three syllogisms which look like the following: We know for a fact that syllogism #1 and #3 are ...
1answer
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### A couple of Natural Deduction proofs

I have two proofs that I can't figure out how to get started on. a) q ├ (p ∨ ¬p) & q b) p ∨ q, p→¬q Ⱶ (p→q)→(q ∧ ¬p) for q ├ (p ∨ ¬p) & q I only assumed that I might try to prove it ...
1answer
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### Use mathematical induction to prove that a function F deﬁned by specifying F (0) and a rule for obtaining F (n+1) from F (n)is well deﬁned.

Im just not sure what the question is asking me to prove, or how to prove it with induction.
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### formal proof - logic

I am trying to prove the following, using natural deduction: $$p\wedge q\Leftrightarrow p \vdash p \Rightarrow q$$ with the following but i seem to get stuck. I know i have to prove $q$, but am not ...
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### Predicate Logic, confusion about implication statement.

Let's say the domain of discourse is the set of 10 balls, numbered as such from 1 to 10. Some (more than 1 but NOT all) of those balls are put into a bag, and then some of those in the first bag are ...
1answer
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### How do I use rules of inferences to imply a conclusion from 4 premises?

I am a little confused on how to use 4 premises to prove a conclusion. Can you please tell me if my logic is sound for the following proof: ...
2answers
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### Formalizing sentences in predicate logic

I would like to formalize "The lecturer is happy, if all his students love logic" using Lecturer as a constant; $H(X) = X$ is happy; $S(X) = X$ is a student; $L(X) = X$ loves logic; $T(X,Y) = X$ ...
3answers
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### Rewrite expressions

I have to prove that $$q\lor(¬q\land(p\lor q))$$ is equal to just $q$. This is normally done with logical equivalences, but I can't solve this one. Can somebody please help? ...
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### Is -1 less than 0.1?

In a High School Maths Test, I presumed that since -1 has as much mathematical mass as a whole unit [-1 x -1 = 1, 1 x 1 = 1] and 0.1 represents one tenth of a unit, that -1 is greater than 0.1 -1 is ...
2answers
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### A quick question about a logical negation

I just want to make sure I'm negating the following logical statement correctly (for a contradiction proof): For every set $A$, there exists a well ordered set $V$ such that there exists no ...
1answer
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### Determine whether each of the following sets is well ordered?

A set is well ordered if every nonempty subset of this set has a least element. Determine whether each of the following sets is well ordered. a) the set of integers b) the set of integers greater ...
1answer
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### Every truth function of the inderterminates X and Y is an iterated composition of negations and disjunctions.

I'm reading K.T.Leung and Doris L.C.Chen's Elementary set theory.I can't solve exercise 10: Prove that every truth function of the inderterminates X and Y is an iterated composition of negations and ...
1answer
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### What is the proper way to format a hypothetical syllogism proof?

Problem: Show that these three statements are equivalent, where $a, b \in R:$ (i) $a < b$, (ii) the average of $a, b,$ is greater than $a,$ and (iii) the average of $a$ and $b$ is less than $b$. ...
1answer
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### Elementary Truth Functional Logic question

So I am currently attacking a question from the first chapter of my logic book. I know that the question is true, but I am having a hard time actually proving it. The question is as follows. If a ...
1answer
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### Completeness of posets

I think this is rather a simple question in order theory, but if someone could explain it step by step that would be really useful. If we have an arbitrary set, then let's denote the set of all finite ...
2answers
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### Are the following statements correctly translated?

Using predicate symbols shown below and appropriate quantifiers, write each English language statement as a predicate wff. Domain is all the objects in world. B(x) : x is a bee F(x) : x is a ...
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### Help with really confusing venn diagram

So this is by far the most confusing venn diagram problem i've ever done. Can someone help me out? I know that Real numbers contain rational, and rational contain integers, but i get really confused ...