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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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
33 views

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.
64 views

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 ...
77 views

In Fitch, how does one prove ¬(B ∧ C) from two premises (A → ¬B) and (¬A → ¬C) [closed]

Help me out please!! I have been trying to solve it for hours
118 views

language logic and proof chapter 12 question 49 and question 50

I've been working on this and I can't seem to figure out what exactly is going wrong can anyone help?
65 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?
31 views

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 ...
148 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
42 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
148 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,...
82 views

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 ...
2k views

fitch proof chapter 13 exercise 13.49 [closed]

Does anyone know how to solve 13.49 ∃x P(x) ∀x ∀y ((P(x) ∧ P(y)) → x = y) = ∃x (P(x) ∧ ∀y (P(y) → y = x)) and 13.50 ∃x (P(x) ∧ ∀y (P(y) → y = x)) = ∀x ∀y ((P(x) ∧ P(y)) → x = y) I have big ...
221 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 ...
46 views

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 ...
137 views

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!
131 views

Fitch-style natural deduction

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

Having trouble with a proof

I have been working on this proof and can't seem to figure out how to do a critical step. I am trying to derive the universal quantifier @x and @y. I have derived @z already. Any help is appreciated ...
163 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). ...