, we should have had
the reduced solution of which is
in which
is an arbitrary elective symbol. This exactly agrees with the former result.
These examples may suffice to illustrate the employment of the method in particular instances. But its applicability to the demonstration of general theorems is here, as in other cases, a more important feature. I subjoin the results of a recent investigation of the Laws of Syllogism. While those results are characterized by great simplicity and bear, indeed, little trace of their mathematical origin, it would, I conceive, have been very difficult to arrive at them by the examination and comparison of particular cases.
Laws of Syllogism deduced from the Elective Calculus.
We shall take into account all propositions which can be made out of the classes