3. Strike out every alternative which is then found to break the Law of Contradiction.
4. The remaining terms may be equated to the term in question as the desired description.
Mr. Venn’s Problem.
The need of some logical method more powerful and comprehensive than the old logic of Aristotle is strikingly illustrated by Mr. Venn in his most interesting and able article on Boole’s logic.[76] An easy example, originally got, as he says, by the aid of my method as simply described in the Elementary Lessons in Logic, was proposed in examination and lecture-rooms to some hundred and fifty students as a problem in ordinary logic. It was answered by, at most, five or six of them. It was afterwards set, as an example on Boole’s method, to a small class who had attended a few lectures on the nature of these symbolic methods. It was readily answered by half or more of their number.
The problem was as follows:—“The members of a board were all of them either bondholders, or shareholders, but not both; and the bondholders as it happened, were all on the board. What conclusion can be drawn?” The conclusion wanted is, “No shareholders are bondholders.” Now, as Mr. Venn says, nothing can look simpler than the following reasoning, when stated:—“There can be no bondholders who are shareholders; for if there were they must be either on the board, or off it. But they are not on it, by the first of the given statements; nor off it, by the second.” Yet from the want of any systematic mode of treating such a question only five or six of some hundred and fifty students could succeed in so simple a problem.
By symbolic statement the problem is instantly solved. Taking
A = member of board
B = bondholder
C = shareholder
the premises are evidently
A = ABc ꖌ AbC B = AB.
The class C or shareholders may in respect of A and B be developed into four alternatives,