In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
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I can't figure out how to prove that formally. Please, help!!
logic proof fitch
edited Nov 26 at 20:42
Frank Hubeny
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asked Nov 26 at 19:44
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I can't figure out how to prove that formally. Please, help!!
logic proof fitch
edited Nov 26 at 20:42
Frank Hubeny
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asked Nov 26 at 19:44
user36043
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I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43
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down vote
favorite
up vote
0
down vote
favorite
I can't figure out how to prove that formally. Please, help!!
logic proof fitch
edited Nov 26 at 20:42
Frank Hubeny
6,22951244
asked Nov 26 at 19:44
user36043
102
I can't figure out how to prove that formally. Please, help!!
logic proof fitch
logic proof fitch
edited Nov 26 at 20:42
Frank Hubeny
6,22951244
asked Nov 26 at 19:44
user36043
102
edited Nov 26 at 20:42
Frank Hubeny
6,22951244
asked Nov 26 at 19:44
user36043
102
edited Nov 26 at 20:42
Frank Hubeny
6,22951244
edited Nov 26 at 20:42
Frank Hubeny
6,22951244
edited Nov 26 at 20:42
Frank Hubeny
6,22951244
6,22951244
asked Nov 26 at 19:44
user36043
102
asked Nov 26 at 19:44
user36043
102
asked Nov 26 at 19:44
user36043
102
102
I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43
add a comment |
I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43
I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43
I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43
add a comment |
2 Answers
2
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up vote
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down vote
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
One assumes not-P and uses a Reduction To Absurdity proof.
|_ (~P v Q) -> P Premise
| |_ ~P Assumption
| | : :
| | : :
| | : :
| ~~P Negation Introduction
| P Double Negation Elimination
answered Nov 26 at 22:34
Graham Kemp
84918
add a comment |
up vote
2
down vote
Here is a way to prove this using the rules in Klement's Fitch-style proof checker. The rules are described in forallx. Both are available in the links below and would make good supplementary material to whatever text you are using.
This proof uses the law of the excluded middle (LEM). To use this I take a simple statement and its negation and from both try to derive the same result. If I get the same result than I can invoke the law of the excluded middle. Here I chose "P" and "¬P", because one of these, "P", is the goal itself.
For "P" I need do nothing but add the subproof with assumption "P". For "¬P" I use disjunction introduction to get line 4 and then conditional elimination on line 5 (modus ponens) to get "P". I reached the goal, "P", in both cases and so I can discharge the two assumptions on line 2 and 3 and reach the end of the proof.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
answered Nov 26 at 20:25
Frank Hubeny
6,22951244
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
One assumes not-P and uses a Reduction To Absurdity proof.
|_ (~P v Q) -> P Premise
| |_ ~P Assumption
| | : :
| | : :
| | : :
| ~~P Negation Introduction
| P Double Negation Elimination
answered Nov 26 at 22:34
Graham Kemp
84918
add a comment |
up vote
3
down vote
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
One assumes not-P and uses a Reduction To Absurdity proof.
|_ (~P v Q) -> P Premise
| |_ ~P Assumption
| | : :
| | : :
| | : :
| ~~P Negation Introduction
| P Double Negation Elimination
answered Nov 26 at 22:34
Graham Kemp
84918
add a comment |
up vote
3
down vote
up vote
3
down vote
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
One assumes not-P and uses a Reduction To Absurdity proof.
|_ (~P v Q) -> P Premise
| |_ ~P Assumption
| | : :
| | : :
| | : :
| ~~P Negation Introduction
| P Double Negation Elimination
answered Nov 26 at 22:34
Graham Kemp
84918
In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
One assumes not-P and uses a Reduction To Absurdity proof.
|_ (~P v Q) -> P Premise
| |_ ~P Assumption
| | : :
| | : :
| | : :
| ~~P Negation Introduction
| P Double Negation Elimination
answered Nov 26 at 22:34
Graham Kemp
84918
answered Nov 26 at 22:34
Graham Kemp
84918
answered Nov 26 at 22:34
Graham Kemp
84918
answered Nov 26 at 22:34
Graham Kemp
84918
84918
add a comment |
add a comment |
up vote
2
down vote
Here is a way to prove this using the rules in Klement's Fitch-style proof checker. The rules are described in forallx. Both are available in the links below and would make good supplementary material to whatever text you are using.
This proof uses the law of the excluded middle (LEM). To use this I take a simple statement and its negation and from both try to derive the same result. If I get the same result than I can invoke the law of the excluded middle. Here I chose "P" and "¬P", because one of these, "P", is the goal itself.
For "P" I need do nothing but add the subproof with assumption "P". For "¬P" I use disjunction introduction to get line 4 and then conditional elimination on line 5 (modus ponens) to get "P". I reached the goal, "P", in both cases and so I can discharge the two assumptions on line 2 and 3 and reach the end of the proof.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
answered Nov 26 at 20:25
Frank Hubeny
6,22951244
add a comment |
up vote
2
down vote
Here is a way to prove this using the rules in Klement's Fitch-style proof checker. The rules are described in forallx. Both are available in the links below and would make good supplementary material to whatever text you are using.
This proof uses the law of the excluded middle (LEM). To use this I take a simple statement and its negation and from both try to derive the same result. If I get the same result than I can invoke the law of the excluded middle. Here I chose "P" and "¬P", because one of these, "P", is the goal itself.
For "P" I need do nothing but add the subproof with assumption "P". For "¬P" I use disjunction introduction to get line 4 and then conditional elimination on line 5 (modus ponens) to get "P". I reached the goal, "P", in both cases and so I can discharge the two assumptions on line 2 and 3 and reach the end of the proof.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
answered Nov 26 at 20:25
Frank Hubeny
6,22951244
add a comment |
up vote
2
down vote
up vote
2
down vote
Here is a way to prove this using the rules in Klement's Fitch-style proof checker. The rules are described in forallx. Both are available in the links below and would make good supplementary material to whatever text you are using.
This proof uses the law of the excluded middle (LEM). To use this I take a simple statement and its negation and from both try to derive the same result. If I get the same result than I can invoke the law of the excluded middle. Here I chose "P" and "¬P", because one of these, "P", is the goal itself.
For "P" I need do nothing but add the subproof with assumption "P". For "¬P" I use disjunction introduction to get line 4 and then conditional elimination on line 5 (modus ponens) to get "P". I reached the goal, "P", in both cases and so I can discharge the two assumptions on line 2 and 3 and reach the end of the proof.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
answered Nov 26 at 20:25
Frank Hubeny
6,22951244
Here is a way to prove this using the rules in Klement's Fitch-style proof checker. The rules are described in forallx. Both are available in the links below and would make good supplementary material to whatever text you are using.
This proof uses the law of the excluded middle (LEM). To use this I take a simple statement and its negation and from both try to derive the same result. If I get the same result than I can invoke the law of the excluded middle. Here I chose "P" and "¬P", because one of these, "P", is the goal itself.
For "P" I need do nothing but add the subproof with assumption "P". For "¬P" I use disjunction introduction to get line 4 and then conditional elimination on line 5 (modus ponens) to get "P". I reached the goal, "P", in both cases and so I can discharge the two assumptions on line 2 and 3 and reach the end of the proof.
Reference
Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
answered Nov 26 at 20:25
Frank Hubeny
6,22951244
answered Nov 26 at 20:25
Frank Hubeny
6,22951244
answered Nov 26 at 20:25
Frank Hubeny
6,22951244
answered Nov 26 at 20:25
Frank Hubeny
6,22951244
6,22951244
add a comment |
add a comment |
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I made an edit which you may roll back or continue editing. Welcome to this SE! Look under the tags you used for other questions and answers on Fitch-style natural deduction.
– Frank Hubeny
Nov 26 at 20:43