[528] The equivalence between this and our former solution is immediately obvious. Equationally it would be written Ab = c.
II. Everything is ACe or aBCe or aBcdE or abCe or abcE ; therefore, by obversion, Nothing is Ac or BcD or CE or ce.
This proposition may be successively resolved as follows:
| ⎧ | No c is A or e, |
| ⎨ | No E is C, |
| ⎩ | No BD is c. |
| ⎧ | All c is aE, |
| ⎨ | All E is c, |
| ⎩ | All BD is C. |
III. Everything is ABCD or ABCd or ABcd or AbCD or AbcD or aBCD or aBcD or aBcd or abCd ; therefore, by obversion, Nothing is ABcD or Abd or aBCd or abc or abD ; and this proposition may be successively resolved as follows:
| ⎧ ⎨ ⎩ | No ABc is D ; |
| No bd is A ; | |
| No aBC is d ; | |
| No ab is c or D. | |
| ⎧ ⎨ ⎩ | All ABc is d ; |
| All bd is a ; | |
| All aBC is D ; | |
| All ab is Cd. |
It is rather interesting to find that notwithstanding the indeterminateness of the problem we obtain by independent methods the same result in each of the above cases.
537. A Third Method of Solution of the Inverse Problem.—The following is a third independent method of solution of the inverse problem, and it is in some cases easier of application than either of the two preceding methods.
532 Any proposition of the form
Everything is ……