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I know that they are equivalent statements from truth tables and common sense, but I have to come to this conclusion via only six mechanisms: elimination of an and; elimination of an or; introduction of an and; introduction of an or; introduction of a contradiction; elimination of a contradiction. To me, this result is so "duh!" but I can't figure out a valid proof. I can't use anything like de Morgan's laws as ... that would be beyond the mechanisms given me. John Riemann Soong ( talk) 00:43, 28 September 2009 (UTC)
(e/c) It's not entirely clear what proof system are you using, but the names of the rules suggest that it's a kind of natural deduction. Nevertheless I'm not quite sure what exactly do you mean by "introduction/elimination of a contradiction". Here's a proof (in sequential form, for typographical reasons):
1. ¬(A ∨ B) [assumption] 2. A [temporary assumption] 3. A ∨ B [∨-introduction from 2] 4. ¬A [reductio ad absurdum from 1 and 3, discarding assumption 2] 5. B [temporary assumption] 6. A ∨ B [∨-introduction from 5] 7. ¬B [reductio ad absurdum from 1 and 6, discarding assumption 5] 8. ¬A ∧ ¬B [∧-introduction from 4 and 7]
If your rules for negation are different, it shouldn't be hard to adjust it; this form of De Morgan's law is intuitionistically valid, hence it should be provable using any reasonable version of negation rules. — Emil J. 11:48, 28 September 2009 (UTC)
I remember reading an article where a person would sell a $1 coin at a market/auction/something and people would "buy" the $1 coin. It shows how a person is forced to outbid the other bidder and thus eventually ends up paying more than the amount of the coin. Know what I'm talking about? :) Deon555 ( talk) 06:49, 28 September 2009 (UTC)
Hi, I have a question about conformal maps from the surface of a sphere unto a square.
Is there a unique mapping (other than for choice of centre and orientation) that can achieve this? Or are there many such mappings?
Thanks.-- Leon ( talk) 21:29, 28 September 2009 (UTC)
Mathematics desk | ||
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< September 27 | << Aug | September | Oct >> | September 29 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
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The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I know that they are equivalent statements from truth tables and common sense, but I have to come to this conclusion via only six mechanisms: elimination of an and; elimination of an or; introduction of an and; introduction of an or; introduction of a contradiction; elimination of a contradiction. To me, this result is so "duh!" but I can't figure out a valid proof. I can't use anything like de Morgan's laws as ... that would be beyond the mechanisms given me. John Riemann Soong ( talk) 00:43, 28 September 2009 (UTC)
(e/c) It's not entirely clear what proof system are you using, but the names of the rules suggest that it's a kind of natural deduction. Nevertheless I'm not quite sure what exactly do you mean by "introduction/elimination of a contradiction". Here's a proof (in sequential form, for typographical reasons):
1. ¬(A ∨ B) [assumption] 2. A [temporary assumption] 3. A ∨ B [∨-introduction from 2] 4. ¬A [reductio ad absurdum from 1 and 3, discarding assumption 2] 5. B [temporary assumption] 6. A ∨ B [∨-introduction from 5] 7. ¬B [reductio ad absurdum from 1 and 6, discarding assumption 5] 8. ¬A ∧ ¬B [∧-introduction from 4 and 7]
If your rules for negation are different, it shouldn't be hard to adjust it; this form of De Morgan's law is intuitionistically valid, hence it should be provable using any reasonable version of negation rules. — Emil J. 11:48, 28 September 2009 (UTC)
I remember reading an article where a person would sell a $1 coin at a market/auction/something and people would "buy" the $1 coin. It shows how a person is forced to outbid the other bidder and thus eventually ends up paying more than the amount of the coin. Know what I'm talking about? :) Deon555 ( talk) 06:49, 28 September 2009 (UTC)
Hi, I have a question about conformal maps from the surface of a sphere unto a square.
Is there a unique mapping (other than for choice of centre and orientation) that can achieve this? Or are there many such mappings?
Thanks.-- Leon ( talk) 21:29, 28 September 2009 (UTC)