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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Formal Proof with Quantifiers
∀x ((Cube(x) ∧ Large(x)) ∨ (Tet(x) ∧ Small(x)))
∀x (Tet(x) → BackOf(x, c))
∀x ¬(Small(x) ∧ Large(x))
goal: ∀x (Small(x) → BackOf(x, c))
How would one prove ∀x (Small(x) → BackOf(x, c)) in a formal ...
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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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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 ...
CommunityBot
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Fitch derivations for equivalence relation properties
Primarily, this a request to check Fitch-style derivations in the file,
https://drive.google.com/file/d/1du-EIZG3CSdrcfDbldlzwgRftDzeVc8K/view?usp=drivesdk
This is not trivial. The reflexiveness ...
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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 :
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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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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Fitch Proof Help, Conclude ~B from ~(A > B) [closed]
I'm in the process of learning fitch proofs and I've come across one I'm having trouble setting up.
Premise: ~(A > B)
Goal: (A & ~B)
In other words, it looks something like this:
1 | ~(A > B)...
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I've been working on this for way too long :/
I've made a lot of progress on the proof below, but I am stuck on the last steps where I need to add existential quantifiers back in: ¬∃x ∃y Smaller(x,y)
For context, I'm a logic novice, but I'm ...
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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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Help with Fitch formal proof?
I'm having trouble solving this formal proof in Fitch. I've put together most of it, but I think I need to use disjunction elim(?) at some point and am having trouble doing that.
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Trying to do proof for ~(A->B) |- A^~B by Fitch Style proof. with Condition do not use de Morgan's law [closed]
Need help to Proof
~(A->B) :- A ^ ~B
I was following William Rose proof from 1 to 33. but I am stuck on this.
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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 proofs help?
I'm new to logic and can see how to write these out informally, but need some help seeing how they should be translated into formal proofs in Fitch.
CommunityBot
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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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Question about proving a set that is quantificationally inconsistent in PD+ (Finished the proof but want it to be checked)
Does ∃x(Nx & ~Nx) contradiction itself?
Is there an error in my proof?
Thank you
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How do I prove ∀x(A(x) -> B(x)) from ~∃x(A(x) ^ ~B(x)) using a fitch proof? [closed]
What would the formal fitch proof for this be? This question came up in my practice problems and I'm really stuck on how to proceed. I'm assuming that you start with an assumption, but I can't figure ...
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Is the included derivation feasible? If so, would my proof be correct?
The simple derivation seems correct and intuitive, and yet I feel as if something is off.
I would greatly appreciate it if someone could double-check the provided formal proof.
Thank you in advance ...
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How does one prove (A->B)vC from the premise ~A? [closed]
Is the premise really enough to prove this?
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How to prove the following arguments [closed]
I'm trying to do a bunch of proofs to get better at them but it seems like I need some help with negation. Can anyone who has time prove the following arguments? I would really appreciate it!
¬(P ∧ ¬Q)...
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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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Validity of the Definiton of the Conditional [closed]
Can a proof for
Premise (P→Q)
...
Goal (¬P∨Q)
be derived using only the following rules?
Conjunction Introduction
Conjunction Elimination Left
Conjunction Elimination Right
Disjunction Introduction ...
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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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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 chapter 13 (ex. 13.29) [closed]
how to proof exercise 13.29 without using taut con
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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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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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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 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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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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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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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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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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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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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.
CommunityBot
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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 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?
CommunityBot
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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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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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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 ...
CommunityBot
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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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