284 Returning to the distinctions indicated in the preceding section, it is hardly necessary to add that if the hypothetical If not X then Y is interpreted modally, while the alternative Either X or Y is interpreted assertorically, then the alternative can be inferred from the hypothetical, but not vice versâ.
EXERCISES.
194. Shew how an alternative proposition in which the alternants are not known to be mutually exclusive (e,g., Either X or Y or Z is true) may be reduced to a form in which they necessarily are so. Write the new proposition in as simple a form as possible. [K.]
195. Shew why the following propositions are not contradictories: Wherever A is present, B is present and either C or B is also present ; In some cases where A is present, either B or C or B is absent. How must each of these propositions in turn be amended in order that it may become the true contradictory of the other? [K.]
196. No P is both Q and R. Reduce this proposition (a) to the form of a conditional proposition, (b) to the form of an alternative proposition. Give the contradictory of the original proposition, of its conditional equivalent, and of its alternative equivalent; and test your results by enquiring whether the three contradictories thus obtained are equivalent to one another. [K.]