# 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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### How to prove a valid argument? (discrete math)

"If I eat all night,then I can get fat.If I get fat then I will have a boyfriend.Therefore,if I eat all night, then I will have a boyfriend." Is the following a valid argument, according to what you ...
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### Negate the statement in discrete math

I need help with the negation in discrete math The question is : Negate the statement and express your answer in a smooth english sentence. Hint first rewrite the statement so that it does not ...
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### binary resolution rule proof

I want to proof the binary resolution rule that is, if we For any two clauses $C_1$ and $C_2$, if there is a literal $L_1$ in $C_1$ that is complementary to a literal $L_2$ in $C_2$, then delete $L_1$ ...
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### ∀x ∈R, ∃y ∈R s.t ∀z ∈R , x + y = z

∀x ∈R, ∃y ∈R s.t ∀z ∈R , x + y = z The above statement is false but I can't figure out why? Or how can I prove that the statement is false?
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### How it can be formally proved that a formula of First Order Logic with identity has only infinite models?

I have an irreflexive and transitive relation $R$. Then I want to prove that $\forall x \exists y (xRy)$ has only infinite models. I have an intuitive idea for which the relation $R$ cannot be ...
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### Real numbers for beginners

I am thinking about the Wikipedia (I understand disputed) article about “definable real numbers”. It begins to say that, A real number $a$ is first-order definable in the language of set theory, ...
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### Relations and logic

$R$ is a relation defined on the set $\mathbb Z$ of integers. For any $a,b \in \mathbb Z$, $a\,R\,b$ iff for any prime number $p$,one has $p\,|\,a$ if and only if $p\,|\,b$. I'm trying to prove or ...
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### Determine the truth value for the predicate (logic)

Im not quite sure how to go about answering these type of questions as the difference of the universal and existential quantifier are confusing me. Hoping someone could explain how to go about ...
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### JAPE double negation handling

I'm trying to prove a simple conjecture using JAPE application. There must be some 'magic trick' in JAPE to get rid of double negation statements but I have no idea how to handle it properly. The ...
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### In logic why can't “p unless q” be “q -> ~p”?

Logically, when I think about p unless q I want to say that it is equivalent to q -> ~p, but the only equivalence is ...
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### theory of semi-algebraic sets

Is there a formal axiomatic way to study semi-algebraic sets? Some facts about them can be deduced by their polynomial structure. Semi-algebraic sets are closed under compliments, intersections, ...
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### Can we do the inductive step without using inductive hypothesis

I wonder if in case I correctly performed first step of induction and next I proved it for n+1, this is still Mathematical Induction? I know, that if I proved it without inductive hypothesis, I could ...
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### Proof completion problem: I can only use primitive rules of inference, and I have contradictory premises.

Standard proof completion: ~(p&q) A ~(~p&q) A ~(p&~q) A ~(~p&~q) A SHOW r Contradicting r and then showing a contradiction seems like the obvious plan of attack, but after that I'm ...
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### Is a logical disjunction statement reversible?

This might be a stupid question, but I'm just learning proofs so I'm unsure. if I have $e \vee f$, can I change it to $f \vee e$ without repercussion?
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### If $A \subseteq B$, then prove by using laws of logic that $(A \times B) \cap (B \times A) = A^2$

I think I know the first step but I need some hints on how to complete it. Let, $(x,y)$ is an element of $(A \times B) \cap (B \times A)$
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### What do I need to learn as prerequisites for logic programming in miniKanren or Prolog?

I'm interested in logic programming for AI. Can I just learn logic programming without any math knowledge? If I couldn't, what do I need to learn?
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### Do we consider the dual concept of the sheaves?

The concept of a sheaf on a topological space X can be veiwed as a projection from a topological E space to X which is a local homeomorphism (it belongs to the category of topological spaces). What's ...
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### BAN logic notation: what does horizontal line mean?

I'm learning BAN logic and trying to understand the notation. The bellow picture is an example form Security Engineering by Ross J Anderson. My question is what does the horizontal line mean? I'm ...
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### Will assuming an undecidable statement result in a consistent system?

If you assume that an undecidable statement in a consistent axiomatic system is true (or false), will that new system also be consistent? For example, does $\mathsf{ZF}$ being consistent imply that ...
I'm just trying to make sure I have this right: (b) Give a proof by contradiction of: “If n is an odd integer, then n 2 is odd.” $n = 2k-1$ $n^2 = (2k-1)^2$ $a = n$ is odd $b = n^2$ is odd Since ...