may be resolved into the two propositions:
| ⎰ | All A is …… |
| ⎱ | All a is …… |
which taken together are equivalent to it; similarly All A is …… may be resolved into the two All AB is ……, All Ab is …… and it is clear that by taking pairs of contradictories in this way we may resolve any given complex proposition into a set of propositions containing no alternative terms. Redundancies must of course as before be as far as possible avoided.
To illustrate this method we may again take the first three examples given in section 535.
I. Everything is ABC or Abc or aBC or abC may be resolved successively as follows:
| ⎰ | All C is AB or aB or ab ; |
| ⎱ | All c is Ab. |
| ⎰ | All bC is a ;[529] |
| ⎱ | All c is Ab. |
[529] Taking BC as our subject we have All BC is A or a, and since this is a merely formal proposition, it may be omitted.
II. Everything is ACe or aBCe or aBcdE or abCe or abcE may be resolved successively as follows:
| ⎰ | All C is Ae or aBe or abe ; |
| ⎱ | All c is aBdE or abE. |
| ⎧ | All C is e ; |
| ⎨ | All c is aE ; |
| ⎩ | All c is Bd or b. |
| ⎧ | All C is e ; |
| ⎨ | All c is aE ; |
| ⎩ | All Bc is d. |
III. Everything is ABCD or ABCd or ABcd or AbCD or AbcD or aBCD or aBcD or aBcd or abCd may be resolved successively as follows: