Questions tagged [fitch]

Frederic Brenton Fitch (1908 – 1987) was an American logician who taught at Yale. He invented the Fitch-style for natural deduction. He is also famous for the paradox of knowability. The tag may also refer to natural deduction proof environments in Fitch-style calculus for giving and checking proofs.

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27 views

Question about fitch 6.19 proving A or C from premises A or B and -B or C

How to prove A or C from premises A or B and -B or C. Am using fitch and have been stuck on this for an hour
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how to prove ‘¬∃xP(x)→(P(a)→Q(a))’ from no premises? fitch

I am totally lost on how to do this... can anyone help? What does it mean? I tried to understand what it means before proof but am totally clueless
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4answers
996 views

Given p ⇒ q and m ⇒ p ∨ q, use the Fitch System to prove m ⇒ q

I have spent about 6 hours now trying to prove this using the Fitch system and I just keep going in circles! Attached is one of the 500 attempts :) I have a feeling it's done fairly simply and ...
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2answers
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How to prove A<—>not A

So basically there are no premises, but the file I have received to start this problem has a contradiction symbol as step one. I’m not sure if this was a mistake or purposeful, and if it was ...
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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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58 views

fitch proof chapter 13 (ex. 13.29) [closed]

how to proof exercise 13.29 without using taut con
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2answers
60 views

Logic – Deduction in Tarski's World (Fitch/LPL 13.22) [closed]

I am trying to use existential elimination to derive Brillig(a) & Tove(a). how would I do this? I have tried to do separate sub proofs to prove both Brillig(a) & Tove(a) but that doesn't work ...
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2answers
71 views

Complex Fitch exercise to prove ∀x.r(x) [closed]

Assume a language with the object constant a and the function constant s. Given r(a), ∀x.(p(x) ⇒ r(s(x))), ∀x.(q(x) ⇒ r(s(x))), and ∀x.(r(x) ⇒ p(x) ∨ q(x)), use the Fitch system with Linear Induction ...
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4answers
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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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3answers
560 views

Fitch Proof - Logic LPL 6.31

I am trying to complete the following proof in Fitch but am completely clueless on how to approach it. Any help would be appreciated! Thanks
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1answer
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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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Trouble with fitch and the use of existential elimination rule [closed]

I am wondering why fitch is not allowing me to use existential elimination for this final step
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LPL 10.26 - Fitch - How to use ∀ Intro and ∃ Elim?

I am using LPL (Language, Proof, and Logic, commonly known as LPL) and the bundled Fitch program. I am trying to solve problem 10.26: 10.26: ∀x Tet(b) ↔ ∃w Tet(b) Looks simple enough, as the ...
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2answers
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Given the premises ∀x.(p(x) ⇒ q(x)) and ∀x.(q(x) ⇒ r(x)), use the Fitch system to prove the conclusion ∀x.(p(x) ⇒ r(x))

I'm not able to move forward from step 4. I've tried Implication Introduction applied to 3 and 4 but nothing happens, any help is much appreciated.
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1answer
60 views

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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1answer
73 views

Use the Fitch system to prove the tautology (p ∨ ¬p). Stalled for days (NOT duplicated)

First of all, please don't close this question cause I don't get the explanation given in: Use the Fitch system to prove the tautology (p ∨ ¬p) I have been trying to solve this exercise for days ...
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Use the Fitch system to prove the tautology (p ∨ ¬p). Stalled for days [duplicate]

I'm having trouble solving this one. I've been stuck in step 9 for days now. Any help is very much appreciated.
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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
176 views

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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2answers
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How can I prove the law of excluded third (p ∨ ¬p)) using Fitch?

Good day. I do not quite understand how I can get ~~p after the 11th line. According to the proof of the law itself (and all reasonable logic) I should get it, and then simplify the expression - but ...
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69 views

How to prove (A v ¬ B), (¬ A v C), (¬ C → B) therefore (¬ D v C)

My idea is to use disjunction elimination on (¬ A v C)to obtain C, and then use disjunction introduction to obtain (¬ D v C), but I'm having a hard time obtaining C.
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1answer
88 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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3answers
94 views

How to prove H → M ¬H → ¬M prove H↔M?

I'm using the program Fitch and I need to make a formal proof for this: H → M ¬H → ¬M Prove: H↔M Any ideas on how to do so?
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4answers
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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
299 views

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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1answer
423 views

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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2answers
120 views

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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2answers
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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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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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How would I go about proving P>Q from the premise (notP v Q)? [duplicate]

A similar question had already been asked, but the solution involves steps I am unfamiliar with. in class, we have only been exposed to intro and elim rules, as well as contradiction rules. Here is ...
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1answer
68 views

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
91 views

Contrapositive Fitch Proof

I can't seem to figure out how to get past this step. Any suggestions?
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4answers
303 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
80 views

How to use use the Fitch System to prove (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q) ⇒ p)?

I'm getting a bit stuck in a tailspin on this one. I'm quite new to logic. I'm not sure how or when we use negation to get P. How then does that connect to (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q)?
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446 views

Language proof and logic Chapter 15 question 16 help

I'm trying to go about solving this problem but I'm having problems even knowing how to approach it. Can someone help me to set it up? Here is the premise: ∀x∀y(x ⊆ y ↔️ ∀z(z ∈ x ⟶ z ∈ y) Here is ...
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2answers
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Given premise ~(P↔Q) how can one derive (~P↔Q) using Fitch?

Given premise ~(P↔Q) derive (~P↔Q) using Fitch-style natural deduction. I thought of simplifying the premise but I am still not able to find an answer. Can someone please help me?
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1answer
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How do you prove (p => q => r) => (p => q) => p => r using the Fitch system?

I'm quite new to logic. Thank you for taking the time to review this post. I tried the following and got to the conclusion I wanted but I was never able to prove the statement.
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1answer
208 views

Fitch Proof - Arrow's logic of preferences

I've been stumped on this one question in particular for several days now and I'm hoping to get some help on where I'm going wrong. Given the following premises: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,...
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1answer
208 views

Fitch Arrow Proofs [closed]

Using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C10 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
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3answers
795 views

How do I apply existential elimination to the following Fitch proof?

I am trying to prove ∀x.∀y.loves(x,y) from Relational Proofs using the Fitch system from Barwise and Etchemendy. I can get as far as line 5, but I cannot figure out how to apply Existential ...
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Fitch Question Please Help Me [closed]

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : [![enter image description here][1]][1] How do I reach this goal? Which rules do I use and with which ...
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2answers
110 views

Fitch Question Help

I'm having trouble understanding quantifiers in proofs. The proof I'm working with is : ¬∀x Tet(x) -- Premise ¬∀x (Tet(x) ∧ Medium(x)) -- Goal How do I reach this goal and also get to the goal ...
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1answer
66 views

Conditional IFF - Not sure what's wrong

"Not a valid application of the rule". I don't think 7 - 8 is something that really needs to be proven beyond a reit, but I feel like you should be able to... I'm quite confused on proving Cube(a) ...
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2answers
109 views

Solving a proof in which the goal is the negation of a variable in 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. A ^ B (A ^ ~C) --> ~D A -> ~C (B ^ E) --> (C v D) ~E I ...
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2answers
3k views

Fitch Proof - LPL Exercise 8.17

I am currently finding the third part of this exercise (Conditional 3) difficult to prove. I was sure that my proof was correct, but the Fitch program is saying otherwise. I am finding it ...
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2answers
75 views

Structure of an if and only if proof

I am trying to get this proof to work out and so far I feel like I have the first part right but I'm stuck on how to get the A→B part.
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3answers
452 views

Fitch Proof Question

I'm having trouble with a proof and I'm not sure if it's valid or not. If it appears to be invalid, we are supposed to assign names to the letters in the proof and check it in a World, but when I do ...
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1answer
360 views

How to Prove P(a) → ∀x(P(x) ∨ ¬(x = a)) using Natural Deduction

How would a formal Fitch proof look like. I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic. I am confused on how to proceed with the proof. Please advice me ...
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244 views

Fitch-style natural deduction

How to prove the following questions? (a) p from assumption ¬(p → q) (b) ¬¬p → p from no assumptions.