that is to say, the number of persons in the house who are aged is at least equal to, and may exceed, the number of male persons in the house;
(ABc) = w′, (2)
that is to say, the number of male persons in the house who are not aged is some unknown positive quantity.
If we develop the terms in (1) by the Law of Duality (pp. [74], [81], [89]), we obtain
(ABC) + (ABc) = (ABC) + (AbC) - w.
Subtracting the common term (ABC) from each side and substituting for (ABc) its value as given in (2), we get at once
(AbC) = w + w′,
and adding (Abc) to each side, we have
(Ab) = (Abc) + w + w′.
The meaning of this result is that the number of persons in the house who are not men is at least equal to w + w′, and exceeds it by the number of persons in the house who are neither men nor aged (Abc).