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, which of the following pairs of statements might either both be true or both be false ?
Looking at each statement individually:
Option A: I and II cannot be both true, and hence option A can be eliminated as an option.
Option B: These two statements can be both true and both false.
Option C: These two directly contradict each other and hence can not be both true.
Option D: These are polar opposite statements and can not be both true.