228. What can be determined respecting a valid syllogism under each of the following conditions: (1) that only one term is distributed, and that only once; (2) that only one term is distributed, and that twice; (3) that two terms only are distributed, each only once; (4) that two terms only are distributed, each twice? [L.]
229. Two propositions are given having a term in common. If they are I and A, shew that either no conclusion or two can be deduced; but if I and E, always and only one. [T.]
230. Find out, from the rules of the syllogism, what are the valid forms of syllogism in which the major premiss is particular affirmative. [J.]
231. Given (a) that the major premiss, (b) that the minor premiss, of a valid syllogism is particular negative, determine in each case the syllogism. [K.]
232. Given that the major premiss of a valid syllogism is affirmative, and that the major term is distributed both in premisses and conclusion, while the minor term is undistributed in both, determine the syllogism. [N.]
233. Shew directly in how many ways it is possible to prove the conclusions SiP, SoP. [W.]
234. Shew that if the rule that a negative conclusion requires a negative premiss be omitted from the general rules of the syllogism, the only invalid syllogism thereby admitted is such that, if its conclusion be false whilst its premisses are true, the three terms of the syllogism must be absolutely coextensive. [O’S.]
235. Find, by direct application of the fundamental rules of syllogism, what are the valid forms of syllogism in which neither of the premisses is a universal proposition having the same quality as the conclusion. [J.]
308 236. In what cases will contradictory major premisses both yield conclusions when combined with the same minor?
How are the conclusions related?
Shew that in no case will contradictory minor premisses both yield conclusions when combined with the same major. [O’S.]
237. (a) All just actions are praiseworthy; (b) No unjust actions are expedient; (c) Some inexpedient actions are not praiseworthy; (d) Not all praiseworthy actions are inexpedient.
Do (c) and (d) follow from (a) and (b)? [K.]