represents AB or aC ;
represents (A or C) and (a or B). But these are equivalent to each other; for (A or C) and (a or B) is equivalent to AB or aC or BC, and—since BC by development is ABC or aBC—this is equivalent to AB or aC. Mr Johnson continues as follows:—“By adopting the plan of placing successive letter-symbols in opposite corners we may solve the inverse problem with surprising ease. The method of solution closely resembles the third of those adopted by Dr Keynes, and it was this that suggested mine. I will, therefore, illustrate by taking Dr Keynes’s three examples which are the following:—
534 Here the columns or determinants may be read off:—
(C or Ab) and (B or a or c) = (If c, then Ab) and (If AC, then B).
This is read: (If c, then aE) and (If BD, then C) and (If C, then e).
That is: (If ab, then Cd) and (If bd, then a) and (If ABD, then C) and (If BCd, then A). In this last problem, we first place B and b opposite; then for the B alternants, we place C and c opposite, and for the b alternants A and a. To get the simplest result, we should aim at dividing the columns into as equal divisions as possible.