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!!










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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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I can't figure out how to prove that formally. Please, help!!










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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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I can't figure out how to prove that formally. Please, help!!










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I can't figure out how to prove that formally. Please, help!!







logic proof fitch






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edited Nov 26 at 20:42









Frank Hubeny

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asked Nov 26 at 19:44









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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




















  • 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












2 Answers
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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





share|improve this answer




























    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.



    enter image description here



    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/






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      2 Answers
      2






      active

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      2 Answers
      2






      active

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      active

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      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





      share|improve this answer

























        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





        share|improve this answer























          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





          share|improve this answer













          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






          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered Nov 26 at 22:34









          Graham Kemp

          81018




          81018






















              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.



              enter image description here



              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/






              share|improve this answer

























                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.



                enter image description here



                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/






                share|improve this answer























                  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.



                  enter image description here



                  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/






                  share|improve this answer












                  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.



                  enter image description here



                  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/







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered Nov 26 at 20:25









                  Frank Hubeny

                  6,05641144




                  6,05641144






















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