Each of the following questions is based on a set of propositions I-IV. Select the best answer to each question.
I. All Ps are Q.
II. Some Ps are not Q.
III. Some, but not all, Ps are Q.
IV. No Ps are Q.
Considered only by themselves, all of the followind pairs of statements might both be false but could not both be true except
Solution
We can check preliminarily for the ability of both statements to be true.
Option A: Both of these statements can not be true. If all Ps are Q, then some Ps can not be Q. Hence, this is not our answer.
Option B: This too can not be true; III can not be true if I is true.
Option C: Both of these can again not be true. If I is true, IV cannot be true.
Option D: This is possible; if no Ps are Q (IV), then some Ps are not Q(II).
Therefore, Option D is the correct answer.
