336. Examine the validity of the following moods:
in figure 1, UAU, YOO, EYO;
in figure 2, AAA, AYY, UOω;
in figure 3, YEE, OYO, AωO. [C.]
337. Enquire in what figures, if any, the following moods are valid, noting cases in which the conclusion is weakened:—AUI; YAY; UOη; IUη; UEO. [L.]
338. If some is used in the sense of “some, but not all,” what can be inferred from the propositions All M is some P, All M is some S? [K.]
339. Giving to some its ordinary logical meaning, shew that, in any syllogism expressed with quantified predicates, a premiss of the form U may always be regarded as a strengthened premiss unless the conclusion is also of the form U. [K.]
340. Is it possible that there should be three propositions such that each in turn is deducible from the other two? [V.]
341. Determine special rules for figures 1, 2, and 4, corresponding to the special rules for figure 3 given in section [329]. [K.]
CHAPTER VIII.
PROBLEMS ON THE SYLLOGISM.
342. Bearing of the existential interpretation of propositions upon the validity of syllogistic reasonings.—We may as before take different suppositions with regard to the existential import of propositions, and proceed to consider how far the validity of the various syllogistic moods is affected by each in turn.