Questions tagged [proof]

For questions about the correctness of a proof or the nature of proofs in general.

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Fitch Formal Logic Help 6.26

6.26 Premise: A v (B ^C) Premise: ~B v ~C v D Goal: A v D Prove it formally without using DeMorgan's Law.
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Fitch Question, Please help! [closed]

Q ∧ S (Q ∧ ¬P) → ¬R Q → ¬P (S ∧ T) → (P ∨ R) The goal is:¬T
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Fitch question, Please help me to proof this [closed]

A → B B → (C→ D) ¬A → (E ∧ F) The Goal is: C → (F ∨ D)
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2answers
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To say that something is a logical consequence is always a subjective statement?

"A mathematically proven statement would be absolutely correct if all the axioms and inference rules used in the proof are first accepted as absolutely correct. That is the whole purpose of creating ...
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fitch proof. P v Q Q→ ¬ R ¬ P ¬ R → ¬ S GOAL: ¬ S

Need help exercise using the FITCH program format. I'm stuck on where to start. The following 4 steps must be used to prove the goal. P v Q Q→ ¬ R ¬ P ¬ R → ¬ S GOAL: ¬ S Now I know: ¬ P and P v Q ...
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Solving a proof with Fitch

I'm working on an assignment and I'm stuck on this proof. I feel like I'm on the right track but I can't find the way to prove the goal. B ^ D (B^¬A) → ¬C B → ¬A (D^E)→ (A v C) GOAL: ¬E
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2answers
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Deductive argument in which every step and premises are explicitly stated?

Is there in philosophy a word/term describing an argument in which all the premises and rules for derivation from those premises are stated explicitly so that even a computer can check it? I know that ...
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1answer
219 views

Using predicate logic, how to solve symmetric and anti reflexive

The networks is: A->B->C->D The channels used by the network are: lo, med, hi h-hi, l-lo, m-med i) A network uses one, and only one channel. ii) Networks within close proximity cannot both use the ...
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Predicate Logic

How do I derive this? Pr 1 ∀x(Fx -> ∀xGx) ∴ ∀x(Fx -> ∀x(Gx \ / Hx)) My attempt: However I cannot used universal derivation due to the free x. I think using ass id and qn would be better ...
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1answer
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Predicate Logic Proof Help! ∃xAx ∨ ∃yFy , ∀x(Ax → Fx) |= ∃xFx [closed]

I am unable to prove it :( I think I need to assume - ∃xFx but what follows later on?
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1answer
154 views

Classification of deductive reasoning types

Please, could you help me make sense of/classify types of deductive reasoning? When studying mathematical logical, I have noticed there is this Hilbert's axiomatic system (Hilbert calculus) with its ...
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1answer
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How to solve this Predicate logic derivation

I want to derive the following: ∀x(Fx ↔ (¬Gx ∨ ¬Hx)). ¬∀x(Gx ∧ Hx) → ∃x(Ix ∧ ¬Gx) ∴ ∃xFx → ∃x(Ix ∧ Fx) This is my attempt: Any suggestions as to how I continue and derive this? I cannot figure out ...
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Use the Fitch system to prove the tautology (p ∨ ¬p)

I've scoured the math stackexchange and the philosophy one for some guidance on how to go about this while using the Fitch System. Anyone can attempt it here; http://logic.stanford.edu/intrologic/...
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fitch arrow proof

using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C7 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
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2answers
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In what contexts or disciplines does “One may assume X” imply “One may ignore the possibility of any statement contrary to X being true”?

In computer programming, it has become fashionable for compilers (processors of computer language) to apply the following form of reasoning: A language standard would permit a compiler to assume that ...
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Language Proof and logic Chapter 13 problem 31

I have been working on this problem for over an hour and I think I have simply missed something. I need some help. I don't see how this is supposed to work out Here are the premises: ∀x ∀y[Likes(x,...
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16answers
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Does a negative claimant have a burden of proof?

I have often heard it said that the burden of proof is on the positive claimant but not on the one making a negative claim. A person claiming, "God exists" has a burden of proof but not a person ...
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1answer
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How would I create a proof In SL

H Therefore, S ⇒(B ⇒H) How would I create a proof in SL which shows the following argument is valid in SL.
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1answer
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De Morgan for Quantifiers Formal Proof: ∀∃-intro and -elim Questions

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
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1answer
124 views

Using the conception of 'reliable, unchanging' does 'truth' exist?

An 'archaic' definition for TRUE,TRUTH implies constancy, reliability, unchanging, fidelity. Using this concept of TRUTH is the following valid? There exists either that which is TRUE or that which ...
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1answer
69 views

Complete a formal proof of ~(~A&~B) from A in as few lines as possible

Prove ~(~A&~B) from A in as few lines as possible. ~ = negation & = conjunction v = disjunction | = line in a subproof Here's what I have: A - Premise |~A - Assume |~B ...
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How do I prove :((A ⊃ B) ⊃ C) ⊃ (B ⊃ C)?

How do I prove, :((A ⊃ B) ⊃ C) ⊃ (B ⊃ C), using symbolic logic derivations where ⊃ represents a conditional i.e. A ⊃ B = A implies B? The first line of my derivations is the assumption, (A ⊃ B) ⊃ C)....
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1answer
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Proving A ⊨ B iff ⊨A → B

Let A and B represent arbitrary formulas. Also let 1 ≡ True and 0 ≡ False Prove that A ⊨ B iff ⊨A → B For my proof, I break down the biconditional into two conditionals and prove each conditional. ...
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2answers
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How do proofs about logic fit into a logical framework?

I'm learning logic from Michael O'Leary's A First Course in Mathematical Logic and Set Theory. In chapter 1 he carefully explains the meaning of logical implication (p ⊨ q), logical inference (p ⟹ q), ...
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Can we logically prove that anything exists?

Suppose I want to prove that negative numbers exist. Well, I could easily do that using a mathematical proof. However, all I would be doing is adding another logical object to a list of known logical ...
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2answers
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How to show (in a hand waving manner) that the Godel sentence is true

I have been reading Graham Priest's The Logic of Paradox, and there is a section where he tried to show that our informal proof argument (in Priest's terminology, naive proof procedure) is more ...
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2answers
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I could prove: Solipsism is wrong. Is my argument acceptable?

Solipsism is the idea that one cannot be sure of anyone's existence but only themself. I think that one can assume this idea to be right and then prove that this is wrong. This self-inconsistency ...
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9answers
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How to prove (A v B), (A → C), (B → D) therefore (C v D)

Obviously since A → C and B → D then if A v B one of C or D must be true. My only idea is v must be introduced, but how would I use subproofs to show one of A /\ C or B /\ D is never false if A v B?
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Does every truth have to be provable based on evidence?

I know the answer is "no" in general due to Gödel's Theory of Incompleteness, but I mean this question in a more real-world sense (i.e. scientific sense). In other words, I am talking about empirical ...
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Language Proof & Logic 8.31 Fitch Proof

Been working on this one question for the past hours and I can't ever seem to get the last step working. Any help would be appreciated!
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1answer
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How do you prove A <-> C given the following premises?

Using the 20-rule proof system (replacement rules, rules of inference, conditional proof, and reductio ad absurdum) and given these 3 premises: A -> ~B ~C -> B ~A -> ~C I know that since I'm ...
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1answer
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Language, Proof and Logic Exercise 14.13 (Fitch)

Having trouble proving this. I know how to prove the first conjunct of the conclusion, but not the second one. Picture shown is the attempt proof of the second conjunct (rules haven't been added yet). ...
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why are ∀x(P(x)→ ∃y(Q(y)∧R(x,y))) and ∃y(Q(y)∧∀x(P(x)→(R(x,y))) not logically equivalent?

been sitting here for hours and still can't figure this out. is the order of ∀x and ∃y important in this case? all I can think of now is "all P is R of some Q", but I don't think this is right.
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Language, Proof, and Logic 14.11 Fitch Proof

Been stuck on this question for awhile now and I just don't know how to get Cube(x) so that I can use ^ intro with Cube(x) and ∀y (Cube(y) → y = a) and then use ∃ intro to get the conclusion. This is ...
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Fitch Proof Exercise 6.20

I am working on a proof and am stuck on a step. I am not sure why I cannot assume the negation of B. Is it not allowed or am I missing something? Thank you]1
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Fitch Proof Help

I'm having some trouble solving this proof in Fitch. How do the universals switch place from the premise to the goal? There is no negation in the goal so negation introduction is not the way to go, I ...
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1answer
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What kinds of proofs can be given for axioms, e.g. the modal axiom S5?

From John Bigelow and Robert Pargetter's book, titled, 'Science and Necessity', they assert the following: . . . . The resulting system, S5, contains all the theorems of S4 and all the theorems of ...
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Fitch Questions Please Help Me

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : How do I reach this goal? Which rules do I use and with which support steps to each rule (proofs to prove ...
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3answers
266 views

Natural deduction proof help!

I've gone through about 40 natural deduction proofs in the past couple days, and mostly they are no problem. For some reason, I've been stuck on 1 tedious problem for an entire day. I just can't seem ...
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4answers
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Does the famous Descartes quote “dubito, ergo cogito, ergo sum” suggests secure knowledge of ones existence?

After a discussion about the "difficulties to distinguish knowledge from faith" someone replied to me that the quote implies faith because it uses the word "think". But as it is generally understood: ...
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3answers
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In Fitch, how does one prove “(P → Q)” from the premise “(¬P ∨ Q)”?

It's all in the question really. I am working on a proof in Fitch for a class, but I am very much stuck. I am proving the tautology that "(P → Q) ↔ (¬P ∨ Q)", and I have already finished half of it, ...
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1answer
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Is a tree proof or natural deduction a semantic method of proof?

Peter Schroeder-Heister writes in an article on "Proof-Theoretic Semantics" the following: Proof-theoretic semantics is inherently inferential, as it is inferential activity which manifests itself ...
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De Morgan's Law Formal Proof [duplicate]

Does anyone know how to do this without the use of addition rules? We have not covered that in class, and all the info I can find online suggests that as a solution. Thanks]1
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1answer
306 views

Proof Using Model Universe

Suppose I am trying to prove the following argument (∀x)(Cx → Dx), (∀x)(Ex → ~Dx), /∴ (∀x)(Ex → ~Cx) Now, let's also assume that I don't know if this argument is valid or not. Because of this, I try ...
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4answers
300 views

In fitch, S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)

Construct a proof for the argument: S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R) I have gotten to the point in the illustration, but I am unable to figure out where to go from here. I get tricked up on ...
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2answers
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Help with an existential natural deduction proof

From the assumption ∃x∃y R(x, y) I need to derive the conclusion ∃y∃x R(x, y) From the comments: I tried to use Existential Elimination but I can't figure out how to do it properly.
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What are some key differences between an argument in logic and a theory in mathematics?

Both are composed from rules and assumptions which enable us to deduce other inevitable truths that results from these rules and assumptions, right?
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1answer
133 views

Are analogical middle terms sufficient for a valid demonstration?

William A. Wallace, O.P., in “Thomism and the Quantum Enigma,” The Thomist 61 (1997): 455–468, claims that analogical middle terms are sufficient for a valid demonstration and that this is a ...
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How does one go about this natural deduction proof?

From no assumptions derive the conclusion ∃x t = x (where t can be any term).
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Are there rules for the following in the Open Logic Project's proof checker?

I'm using http://proofs.openlogicproject.org/ but can't find out what the translation of the rules are. I'm new at this, so when I try to make proofs, I know what I want the justification to be (which ...

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