42. Can a false conclusion be reached through true premises, or a true conclusion through false premises? Give reasons for your answer. [S]
43. Can we under any circumstances infer a relation between X and Z from the premises—
Some Y's are X's
Some Y's are Z's? [S]
44. Take an apparent syllogism subject to the fallacy of negative premises, and inquire whether you can correct the reasoning by converting one or both of the premises into the affirmative form. [S]
45. Enumerate the faults to which a syllogism is liable, giving instances of each. [S]
46. State any Enthymeme, and expand it into (1) a Syllogism, (2) an Epicheirema, (3) a Sorites; and give in each case the technical name of the Mood or Order that results.
47. State any Disjunctive Syllogism, and change it (1) into a Hypothetical, (2) into a Categorical; and discuss the loss or gain, in cogency or significance involved in this process.
48. Can the Syllogism be treated as merely a consequence of the "Laws of Thought"? If not, why not; and what else does it imply?
49. Prove that with three given propositions (of the forms A., E., I., O.) it is never possible to construct more than one valid syllogism. [C]