# Tagged Questions

Questions about mathematical logic, including model theory, proof theory, computability theory (a.k.a. recursion theory), and non-standard logics. Questions which merely seek to apply logical or formal reasoning to other areas of mathematics should not use this tag. Consider using one of the ...

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### Are truth tables a valid method to prove an iff statement?

I recently had a homework assignment returned to me (for a Differential Geometry course, undergrad level) in which my instructor wrote "You cannot use truth tables to prove an if and only if statement"...
2answers
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### truth table of equivalence relation

I have found the following problem in a book: Test the validity of the following argument: If 6 is not even, then 5 is not prime But 6 is even Therefore, 5 is prime I have made a truth table by ...
1answer
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### Prove that for all elements n that are member on set N, 0*1 + 1*2 + 2*3 +…+ n(n+1) = n(n+1)(n+2)/3

The problem is :Prove that for all elements n that are member on set N, 0*1 + 1*2 + 2*3 +....+ n(n+1) = n(n+1)(n+2)/3 I have established a base case for n=0, 0*1 = 0(0+1)(0+2)/3 = 0 I have also ...
2answers
333 views

### Proofs for Relational Predicate Logic --Difficult Question!

I have been working on this problem for four and a half hours and I think I have simply missed something. I need the help of my peers here. The rules I am allowed to use are the Basic Inference rules (...
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1answer
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### $LK-\Phi$ proof of $\exists y Pby$

I am having difficulty with the concept of $LK-\Phi$ proofs, here is a question I have been working on: Let $\Phi = \{Pafa\}$, where $P$ is a binary predicate symbol and $f$ is a unary function ...
4answers
247 views

### “Logically equivalent formulae express the same _______.” <- What word do logicians use for the blank?

Meaning denotes the truth conditions of a sentence: what would have to be the case for the interpreted formula to be true. Nevertheless, without an interpretation, two logically equivalent formulae ...
4answers
624 views

### Conjectures which can't be right or wrong

Recently I was talking with some of my non-mathematician friends. On some very unrelated subject in order to make my point I said: "There are some conjectures in mathematics which are proven to be ...
1answer
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### Find propositional formulas $\phi$ and $\psi$ such that $(\phi \rightarrow (\psi \rightarrow (¬\psi)))$ is a theorem of L.

Find propositional formulas $\phi$ and $\psi$ such that $(\phi \rightarrow (\psi \rightarrow (¬\psi)))$ is a theorem of L. So every axiom is a theorem of L so I thought there would be some way to ...
2answers
74 views

### Suppose $\phi$ is a formula of L. Give a proof in L of the formula $(\phi \rightarrow \phi)$ explaining each step of the proof.

Suppose $\phi$ is a formula of L. Give a proof in L of the formula $(\phi \rightarrow \phi)$ explaining each step of the proof. I have the axioms (A1) $(\phi \rightarrow ( \psi \rightarrow \phi))$ (...
3answers
236 views

### ZFC Axioms to be extended?

Sorry if this is going to be a really loaded question. I was told several times that for virtually all theorems/corollaries/propositions of mathematics (except those cases not compatible with ZFC ...
2answers
55 views

### Gives regular expressions which defines regular language and what does {1,2} mean

The question is give a regular expression which defines a regular language. Question: The language over {0,1} consisting of all strings which either have length less than 3 or have 0 as their third ...
1answer
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1answer
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### How to prove $\vdash (\forall v_1 \,\exists v_2\, fv_1=v_2)$

f is a one-place function symbol. I just don't know where to start. $\forall v_1 \,\exists v_2\, fv_1=v_2$ might come from $\exists v_2 \,fv_1=v_2$ Then I don't know how to deal with the "exists"
2answers
215 views

### How can the Gödel sentence be Pi_1

The Gödel sentence must be provable or unprovable by itself - you have to resolve all definitions until it only uses the elementary symbols of Peano arithmetic. What is the correct way to resolve ...
0answers
48 views

### Linear regression, reversing it back then.

Need's formatting, editing will take some time.
1answer
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### Show that $(\forall x)(A \lor B) \rightarrow A \lor (\forall x)B$ is, in general, NOT a theorem.

Show that $$(\forall x)(A \lor B) \rightarrow A \lor (\forall x)B$$ is, in general, NOT a theorem. My answer: First, I got the abstraction of the formula which is $p \rightarrow A \lor q$ then ...
1answer
111 views

### Do all contradictory statements entail something self-referential?

"The house is all blue(B), and the house is all white(W)" Those statements are, ostensibly, not of the form p ⋀ ¬p. However, they do seem to entail p ⋀ ¬p. For example "The house is all blue" entails ...
1answer
33 views

### Can covering be done on two elements?

The covering rule is: $$B \bullet (B+C) = B$$ and $$B+(B \bullet C)=B$$ So does it follow from this rule that: B \bullet A \bullet \bar{C} + B \bullet D \bullet\bar{F} = B \bullet (A\bullet\bar{C}+D\...
1answer
1k views

### $(p \implies q) \wedge (q \implies r) \implies (p \implies r)$

Show that $(p \implies q) \wedge (q \implies r) \implies (p \implies r)$ is a tautology. I have the truth tables but cannot algebraically manipulate the language itself to prove it. What I ...