Our set of propositions may therefore be expressed as follows:—
| ⎧ ⎨ ⎩ | All AB is D, |
| All ab is c, | |
| All cd is ab, | |
| All D is AB.[531] |
[531] Restoring the second of these propositions to the form All ab is cd, and writing the propositions equationally, the solution may be expressed in a still simpler form, namely, AB = D, ab = cd.
541. Resolve the proposition Everything is ABCDeF or ABcDEf or AbCDEF or AbCDeF or AbcDeF or aBCDEf or aBcDEf or abCDeF or abCdeF or abcDef or abcdef into a conjunction of relatively simple propositions.
[Jevons, Principles of Science, 2nd ed., p. 127 (Problem x.)]
The following is a solution:—
| (1) All A is D ; |
| (2) All ABC is e ; |
| (3) All aF is bCe ; |
| (4) All Bf is DE ; |
| (5) All bf is ace ; |
| (6) All cF is be. |
This is somewhat less complex than the solution by Dr John Hopkinson given in Jevons, Studies in Deductive Logic, p. 256, namely:—
| (i) | All d is ab ; |
| (ii) | All b is AF or ae ; |
| (iii) | All Af is BcDE ; |
| (iv) | All E is Bf or AbCDF ; |
| (v) | All Be is ACDF ; |
| (vi) | All abc is ef ; |
| (vii) | All abef is c. |
537 542. How many and what non-disjunctive propositions are equivalent to the statement that “What is either Ab or bC is Cd or cD, and vice versâ”? [Jevons, Studies, p. 246.]