Thus, AB and BA have the same signification. It comes to the same thing whether out of the class A we select the B’s or out of the class B we select the A’s.
Again, A or B and B or A have the same signification. It is a matter of indifference whether we form a class by adding the B’s to the A’s or by adding the A’s to the B’s.
426. The Opposition of Complex Terms.—However complex a term may be, the criterion of contradictory opposition given in section [40] must still apply: “A pair of contradictory terms are so related that between them they exhaust the entire universe to which reference is made, whilst in that universe there is no individual of which both can be affirmed at the same time.” In what follows it will be found convenient to denote the contradictory of any simple term by the corresponding small letter. Thus for not-A we may write a, and for not-B we may write b.
Now whatever is not AB must be either a or b, whilst nothing that is AB can be either a or b. Hence
⎰ AB,
⎱ a or b,
constitute a pair of contradictories. Similarly,
⎰ A or B,
⎱ ab,
are a pair of contradictories. And the same will hold good if A and B stand for terms which are already themselves complex (although relatively simple as compared with AB or A or B).
If, then, two terms are conjunctively combined into a complex term (of which they will constitute the determinants), the contradictory of this complex term is found by alternatively combining the contradictories of the two determinants. And, conversely, if two terms are alternatively combined into a complex term (of which they will constitute the alternants), the contradictory of this complex term is found conjunctively combining the contradictories of the two alternants.
In each case, we substitute for the relatively simple terms involved their contradictories, and (as the case may be) change 471 conjunctive combination into alternative combination, or alternative combination into conjunctive combination.