| ⎰ | All B is ACD or ACd or Acd or aCD or acD or acd ; |
| ⎱ | All b is ACD or AcD or aCd. |
| ⎰ | All B is AC or aD or cd ; |
| ⎱ | All b is AD or aCd. 533 |
| ⎧ ⎨ ⎩ | All BC is A or aD ; |
| All Bc is aD or d ; | |
| All Ab is D ; | |
| All ab is Cd. | |
| ⎧ ⎨ ⎩ | All BCd is A ; |
| All ABc is d ; | |
| All Ab is D ; | |
| All ab is Cd. |
The above solutions are practically the same as those obtained in the two preceding sections.
538. Mr Johnson’s Notation for the Solution of Logical Problems.—In his articles on the Logical Calculus Mr Johnson proposes a notation by the aid of which the solution of inverse problems may be facilitated. It consists in representing conjunctive combination by horizontal juxtaposition, and alternative combination by vertical juxtaposition. A bar—drawn horizontally or vertically—serves the purpose of a bracket where necessary. Thus,
represents AB or CD;
represents (A or C) and (B or D). These two forms are of course not equivalent to each other. But if contradictories are placed in a pair of diagonally opposite corners, then the combination is the same in whichever way we read it. Thus,
