Difficulty: Easy
Correct Answer: None follows
Explanation:
Introduction / Context:
This item checks your understanding of what can be guaranteed from two independent some-type statements. A common mistake is to chain two overlaps through a middle class and conclude an overlap between the outer classes. Without explicit linkage, that inference is not valid.
Given Data / Assumptions:
Concept / Approach:
A statement of the form some A are B only ensures a nonempty intersection between A and B. Two such statements sharing a middle term (here M) do not force the outer sets to overlap. Therefore conclusions asserting no or some between C and B must be rejected unless forced by the premises. Universal statements like all M are B are also not justified by a mere some relation.
Step-by-Step Solution:
Verification / Alternative check:
Model: Let M = {m1, m2}. Let C = {m1}. Let B = {m2}. Then some C are M (via m1) and some M are B (via m2) hold, while I–IV are all false or not forced, confirming that none follows.
Why Other Options Are Wrong:
Common Pitfalls:
Assuming transitivity for some-statements; overlooking that IV directly contradicts the first premise.
Final Answer:
None follows
Discussion & Comments