All X is P1 or P2 …… or Pm,
All X is Q1 or Q2 …… or Qn,
may for our present purpose be taken as types of universal affirmative propositions having the same subject. By conjunctively combining their predicates, thus,
All X is (P1 or P2 … or Pm) and also (Q1 or Q2 … or Qn),
that is, All X is P1Q1 or P1Q2 … or P1Qn
or P2Q1 or P2Q2 … or P2Qn
or ……
……
or PmQ1 or PmQ2 … or PmQn, 499
we may obtain a new proposition which is equivalent to the conjunctive combination of the two original propositions; it sums up all the information which they jointly contain, and we can pass back from it to them.
In almost all cases of the conjunctive combination of terms there are numerous opportunities of simplification; and, after a little practice, the student will find it unnecessary to write out all the alternants of the new predicate in full. The following are examples:—
| (i) | All X is AB or bce, |
| All X is aBC or DE ; | |
| therefore, | All X is ABDE. |
It will be found that all the other combinations in the predicate contain contradictories.
| (ii) | All X is A or Bc or D, |
| All X is aB or Bc or Cd ; | |
| therefore, | All X is ACd or aBD or Bc. |
| (iii) | Everything is A or bd or cE, |
| Everything is AC or aBe or d ; | |
| therefore, | Everything is AC or Ad or bd or cdE. |
(2) Universal affirmatives having different subjects.
Given the conjunctive combination of two universal affirmative propositions with different subjects, a new complex proposition may be obtained by conjunctively combining both their subjects and their predicates. Thus, if All X is P1 or P2 and All Y is Q1 or Q2, it follows that All XY is P1Q1 or P1Q2 or P2Q1 or P2Q2. But in this case the new proposition obtained is not equivalent to the conjunctive combination of the original propositions; and we cannot pass back from it to them.