# 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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### 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 can I prove a contradiction follows from P <-> Q and P -> ~Q?

I am so close to solving this problem: (Language Logic and Proof 8.36). https://i.stack.imgur.com/1zMnZ.jpg All I need to do to complete the proof is show that P <-> Q and P -> ~Q is a ...
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### 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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### Fitch style disjunction elimination

I am having difficulty in formally proving a simple argument. Consider P(x) v Q(x) not P(x) ---------- Q(x) It is easy to see that the argument is indeed valid, but I cannot seem to prove it ...
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### 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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### Disjunctive Syllogism in a Fitch Style System

I'm trying to prove an argument of the form: B ~(C & B) Therefore: ~C. I can expand out ~(C & B) into ~C OR ~B, and with the premise B, it is clear that ~C is the case. ...
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### Prove A ∨ D from A ∨ (B ∧ C) and (¬ B ∨ ¬ C) ∨ D ( LPL Q6.26) without using --> or material implication

This is a repeated question: Language Logic and Proof Q. 6.26 Using the natural deduction rules, give a formal proof of A ∨ D from the premises A ∨ (B ∧ C) (¬ B ∨ ¬ C) ∨ D ...
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### 2 simple Formal Fitch Proofs

I'm having difficulty proving these. They seem obvious, but I can't figure how to set up formal proofs for them. Could anyone give me clues on how to start them? ¬(P∧¬Q) from the premise P→Q; ¬Q→(R→P)...
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### 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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### Formal proof : predicate logic

This is what I need to prove formally: 1.∃x Cube(x) ∧ Small(d) . . . . Goal :∃x (Cube(x) ∧ Small(d)) I have already tried different ways, but I still can't prove the goal. 1. ∃x Cube(x) ∧ Small(d) ...
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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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### How to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’

What would a formal Fitch proof for this look like? I am given ¬∀x(P(x)→Q(x)), and need to derive ∃xP(x) from it. I started with this, but I don't know if I am doing the right thing, and where to go ...
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### 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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### Conditional disjunction equivalence proof using FItch

Prove P v Q ⇔ ¬Q → P So far I have the obvious things... 1. P v Q _ | 2. ¬Q | _ | 3. | 4. | 5. | 6. | 7. | 8. P 9. ¬Q → P → Intro 2-8 I think the problem here is that I do not ...
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### 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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### Prove ¬∃x ∀y (E(x, y) ↔ ¬E(y, y)) given no premises

The only way I could think of to do this problem is reductio, but since the two biconditional terms are not contradictory, I am pretty stuck.
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### 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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### How does one prove ‘(B→C)→¬A’ from ‘(A→B)∨C’ and ‘(A→¬C)’ in Fitch?

I am trying to work my way through this Fitch proof, and I am not sure what I am doing wrong, but I keep getting stuck no matter what I try. First attempt: Second attempt:
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### Why is the use of the ND rule ∃E not correct in this proof?

Is there anyone who could explain to me why these errors occur? It seems to me the rule was used properly.
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### Fitch Biconditional Proof Help?

Hi, I'm starting to learn formal proofs using Fitch, but I'm having a bit of trouble figuring out my arguments. I've generally mapped out the subproofs I was considering to use, but I'm unsure how to ...
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### 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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### prove: ∃x ∃y (Cube(x) ∧ Cube(y) ∧ x ≠ y ∧ ∀z (Cube(z) → (z = x ∨ z = y)))

I need a formal (Fitch) first order logic proof for: ∃x ∃y (P(x) ∧ P(y) ∧ x ≠ y ∧ ∀z (P(z) → (z = x ∨ z = y))) Given ∃x ∃y (P(x) ∧ P(y) ∧ x ≠ y) ∀x ∀y ∀z ((P(x) ∧ P(y) ∧ P(z)) → (x = y ∨ x = z ∨...
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### Contrapositive Fitch Proof

I can't seem to figure out how to get past this step. Any suggestions?
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### I am stuck on how to prove the contradiction of R(b,a) can anybody help me?

Here are some well-known properties of dyadic (2-place) relations: ∀xR(x, x) (Reflexivity) ∀x¬R(x, x) (Irreflexivity) ∀x∀y(R(x, y) → R(y, x)) (Symmetry) ∀x∀y(R(x, y) → ¬R(y, x)) (Asymmetry) ∀x∀y∀...
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### Suppose A is a set of premises of an argument and B the conclusion of that argument. Prove that if A U {¬B} ⊢ ⊥, then A ⊢ B

Suppose A is a set of premises of an argument and B the conclusion of that argument. Prove that if A U {¬B} ⊢ ⊥, then A ⊢ B. (Use Fitch) I have no idea where to start, can someone help?
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### How to prove : (( P → Q ) ∨ ( Q → R )) by natural deduction

Here's another of Tomassi's exercises I can't solve (Logic, page 106): : (( P → Q ) ∨ ( Q → R )) I have to use natural deduction and the only rules I know are: • assumptions, • modus ponendo ...
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### How would I deduce a≠c from a≠b and b≠c in Fitch?

How would I deduce a≠c from the premises a≠b and b≠c in Fitch? This is what I've done so far. b=b (=Intro) b≠a (Ana Con) b≠c (Reit) And then for some reason I get stuck here? I know this sounds ...
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### Language Logic Proof Question: ¬∃x∀y[E(x,y) ↔ ¬E(y,y)]

I am wondering if I have completed this proof properly. I don't think I have it right. It's tricky! Conclusion: ¬∃x∀y[E(x,y) ↔ ¬E(y,y)] ¬¬∃x∀y[E(x,y) ↔ ¬E(y,y)] ∃x∀y[E(x,y) ↔ ¬E(y,y)] ¬E,1 ...
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### Fitch Proof - Logic LPL 13.11

I am currently doing questions for my course from LPL Chapter 13.11. I have posted the screenshot of what I am trying to do. I am quite stuck and I can not think of a way to get to ~Tet(a). Any hint ...
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### 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 ...
1 vote
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### Symbolic Logic - Quantifier Proof (w/ Conditionals)

I'm not sure if lines 6 - 7 & 8 - 11 are being done correctly. I feel like it's necessary to prove 12 which proves the rest of the problem. I'm a bit stuck on lines 8 - 11. I initially tried to ...
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### 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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### LPL ( language proof and logic) - FITCH - 14.12

what's wrong with the last line in my proof? i can't understand the error on line 21 i wrote the important line of the proof : 18 - ∀z (Cube(z) → (z = c ∨ z = f)) 19 - ∃y (Cube(c) ∧ Cube(y) ∧ c ≠ ...
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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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### trouble with rules of inference practice problems [closed]

Prove the following symbolized arguments applying the appropriate rules of inference: 1) P ∨ Q = M ⊃ ¬ Q M =conjunction Therefore P 2) (P V Q) ∧ ¬ Q P ⊃ R =...
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### Fitch Proof by Contradiction help

Hi, I'm pretty new to writing formal proofs and I was wondering if I could get some help solving this question. I've set up the problem and I was thinking of perhaps proving it by contradiction that ...
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### Symbolic Conditional Help

Premise: (Tet(a) ^ Tet(b)) v (Cube(c) ^ Cube(d)) Cube(c) -> Dodec(e) Goal: ~Tet(a) -> Dodec(e) Anyone have a clue on where to start with this?
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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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### 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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### 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) ...
1 vote
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### Prove transitivity in Fitch

How to prove transitivity in Fitch. Is it Ok? | 1. a = b | 2. b = c | 3. c = c =Intro | 4. a = c =Elim: 3, 2 | 5. b = c =Elim: 4, 1
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### Assume: (C∧D)∨(¬C∧D); Prove: C↔D

Is it possible to prove this formally in fitch? I found that when C is false and D is true the conclusion is false while the premise is true.
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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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### How did Fitch's opposition to the Russell-Whitehead theory of types turn out since the 1950's?

In a footnote to Appendix C of Frederic Fitch's Symbolic Logic (page 217), Fitch writes about his article, "Self-Reference in Philosophy": It is reprinted here in order to indicate more fully my ...
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### Logic – Deduction in Tarski's World (Fitch/LPL 13.36)

I am working on proving the following question: | ∀x [Dodec(x) → LeftOf(x, a)] | ∀x [Tet(x) → RightOf(x, a)] |––– | ∀x [SameCol(x, a) → Cube(x)] The question has the following rules: […] give a ...
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### In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?

I can't figure out how to prove that formally. Please, help!!
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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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### Does rejecting the law of the excluded middle mean rejecting it for all propositions or only for those one cannot derive?

Wikipedia describes the law of the excluded middle as such: In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is ...
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