483. Reduce the propositions All P is Q, No Q is R to such a form that the universe of discourse appears as the subject of each of them; and then combine the propositions into a single complex proposition. How is your result related to the ordinary syllogistic conclusion No P is R? [K.]
484. Combine the following propositions into a single equivalent complex proposition: All X is either A or b ; No X is either AC or acD or CD ; All a is B or x. [K.]
485. Every voter is both a ratepayer and an occupier, or not a ratepayer at all; If any voter who pays rates is an occupier, then he is on the list; No voter on the list is both a ratepayer and an occupier.
Examine the results of combining these three statements. [V.]
486. Every A is BC except when it is D ; everything which is not A is D ; what is both C and D is B ; and every D is C. What can be determined from these premisses as to the contents of our universe of discourse? [M.]
CHAPTER V.
INFERENCES FROM COMBINATIONS OF COMPLEX PROPOSITIONS.
487. Conditions under which a universal proposition affords information in regard to any given term.—The problem to be solved in order to determine these conditions may be formulated as follows: Given any universal proposition, and any term X, to discriminate between the cases in which the proposition does and those in which it does not afford information with regard to this term.
In the first place, it is clear that if the proposition is to afford information in regard to any term whatever it must be non-formal. If it is negative, let it by obversion be made affirmative. Then it may be written in the form
Whatever is A1A2 … or B1B2 … or &c. is P1P2 … or Q1Q2 … or &c.,