How to proof B from a premise in which B does not occur using natural deduction?
I am preparing for my first logic exam and in the test examples I've come across the following question:
Prove by natural deduction:
B from premise A ∧ ¬A
I am unsure how to proceed in formulating this proof as B does not bear any relation to the premise. Does someone know how to proceed in such a proof, what can I assume about B's relation to the premise?
logic natural-deduction
asked Dec 8 at 17:19
Stan Van Der Bend
82
add a comment |
I am preparing for my first logic exam and in the test examples I've come across the following question:
Prove by natural deduction:
B from premise A ∧ ¬A
I am unsure how to proceed in formulating this proof as B does not bear any relation to the premise. Does someone know how to proceed in such a proof, what can I assume about B's relation to the premise?
logic natural-deduction
asked Dec 8 at 17:19
Stan Van Der Bend
82
Use EFQ aka $bot$-elim.
– Mauro ALLEGRANZA
Dec 8 at 17:21
@MauroALLEGRANZA Thanks for the quick reply. I just looked at a short video where they do an example proof using that principle. (youtube.com/watch?v=KvrJYZb595Y) I tried doing something similar to that video in fitch where I assumed B to be a premise alongside the given premise with as goal B. However, even without proving anything fitch already accepts B as true (as I assumed it was.) Do you know what would be the premise for this proof? EDIT: okay nvm I have to make a subproof for B. Thank you once again, I think I got it now :)
– Stan Van Der Bend
Dec 8 at 17:31
add a comment |
I am preparing for my first logic exam and in the test examples I've come across the following question:
Prove by natural deduction:
B from premise A ∧ ¬A
I am unsure how to proceed in formulating this proof as B does not bear any relation to the premise. Does someone know how to proceed in such a proof, what can I assume about B's relation to the premise?
logic natural-deduction
asked Dec 8 at 17:19
Stan Van Der Bend
82
I am preparing for my first logic exam and in the test examples I've come across the following question:
Prove by natural deduction:
B from premise A ∧ ¬A
I am unsure how to proceed in formulating this proof as B does not bear any relation to the premise. Does someone know how to proceed in such a proof, what can I assume about B's relation to the premise?
logic natural-deduction
logic natural-deduction
asked Dec 8 at 17:19
Stan Van Der Bend
82
asked Dec 8 at 17:19
Stan Van Der Bend
82
asked Dec 8 at 17:19
Stan Van Der Bend
82
asked Dec 8 at 17:19
Stan Van Der Bend
82
asked Dec 8 at 17:19
Stan Van Der Bend
82
82
Use EFQ aka $bot$-elim.
– Mauro ALLEGRANZA
Dec 8 at 17:21
@MauroALLEGRANZA Thanks for the quick reply. I just looked at a short video where they do an example proof using that principle. (youtube.com/watch?v=KvrJYZb595Y) I tried doing something similar to that video in fitch where I assumed B to be a premise alongside the given premise with as goal B. However, even without proving anything fitch already accepts B as true (as I assumed it was.) Do you know what would be the premise for this proof? EDIT: okay nvm I have to make a subproof for B. Thank you once again, I think I got it now :)
– Stan Van Der Bend
Dec 8 at 17:31
add a comment |
Use EFQ aka $bot$-elim.
– Mauro ALLEGRANZA
Dec 8 at 17:21
@MauroALLEGRANZA Thanks for the quick reply. I just looked at a short video where they do an example proof using that principle. (youtube.com/watch?v=KvrJYZb595Y) I tried doing something similar to that video in fitch where I assumed B to be a premise alongside the given premise with as goal B. However, even without proving anything fitch already accepts B as true (as I assumed it was.) Do you know what would be the premise for this proof? EDIT: okay nvm I have to make a subproof for B. Thank you once again, I think I got it now :)
– Stan Van Der Bend
Dec 8 at 17:31
Use EFQ aka $bot$-elim.
– Mauro ALLEGRANZA
Dec 8 at 17:21
Use EFQ aka $bot$-elim.
– Mauro ALLEGRANZA
Dec 8 at 17:21
@MauroALLEGRANZA Thanks for the quick reply. I just looked at a short video where they do an example proof using that principle. (youtube.com/watch?v=KvrJYZb595Y) I tried doing something similar to that video in fitch where I assumed B to be a premise alongside the given premise with as goal B. However, even without proving anything fitch already accepts B as true (as I assumed it was.) Do you know what would be the premise for this proof? EDIT: okay nvm I have to make a subproof for B. Thank you once again, I think I got it now :)
– Stan Van Der Bend
Dec 8 at 17:31
@MauroALLEGRANZA Thanks for the quick reply. I just looked at a short video where they do an example proof using that principle. (youtube.com/watch?v=KvrJYZb595Y) I tried doing something similar to that video in fitch where I assumed B to be a premise alongside the given premise with as goal B. However, even without proving anything fitch already accepts B as true (as I assumed it was.) Do you know what would be the premise for this proof? EDIT: okay nvm I have to make a subproof for B. Thank you once again, I think I got it now :)
– Stan Van Der Bend
Dec 8 at 17:31
add a comment |
1 Answer
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Here is a proof in the logic software program Fitch:
answered Dec 9 at 19:35
Bram28
60k44489
add a comment |
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1 Answer
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1 Answer
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active
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active
oldest
votes
active
oldest
votes
Here is a proof in the logic software program Fitch:
answered Dec 9 at 19:35
Bram28
60k44489
add a comment |
Here is a proof in the logic software program Fitch:
answered Dec 9 at 19:35
Bram28
60k44489
add a comment |
Here is a proof in the logic software program Fitch:
answered Dec 9 at 19:35
Bram28
60k44489
Here is a proof in the logic software program Fitch:
answered Dec 9 at 19:35
Bram28
60k44489
answered Dec 9 at 19:35
Bram28
60k44489
answered Dec 9 at 19:35
Bram28
60k44489
answered Dec 9 at 19:35
Bram28
60k44489
60k44489
add a comment |
add a comment |
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Use EFQ aka $bot$-elim.
– Mauro ALLEGRANZA
Dec 8 at 17:21
@MauroALLEGRANZA Thanks for the quick reply. I just looked at a short video where they do an example proof using that principle. (youtube.com/watch?v=KvrJYZb595Y) I tried doing something similar to that video in fitch where I assumed B to be a premise alongside the given premise with as goal B. However, even without proving anything fitch already accepts B as true (as I assumed it was.) Do you know what would be the premise for this proof? EDIT: okay nvm I have to make a subproof for B. Thank you once again, I think I got it now :)
– Stan Van Der Bend
Dec 8 at 17:31