Question

Question below has a three statement, followed by four conclusions numbered I, II, III and IV. You have to consider every given statement as true, even if it does not conform to the well known facts. Read the conclusions and then decide which of the conclusions can be logically derived.
Statements:
I. Some toys are pens.
II. Some pens are papers.
III. Some papers are black.
Conclusions:
I. Some toys are black.
II. No pen is black.
III. No toy is black.
IV. Some pens are black.

• A. None follows
• B. Either II or IV
• C. Either I or III and either II or IV
• D. Either I or IV

Answer 1

The Correct Option is C

To determine which conclusions can be logically derived from the given statements, we must analyze each step:

Statements:
I. Some toys are pens.
II. Some pens are papers.
III. Some papers are black.

Conclusions:
I. Some toys are black.
II. No pen is black.
III. No toy is black.
IV. Some pens are black.

Analysis:
1. There is no direct link between toys and black objects through the given statements. Hence, it is not certain that some toys are black (Conclusion I), nor is it certain that no toys are black (Conclusion III).
2. Since we have some pens that are papers and some papers are black, it might be possible that some pens are black (Conclusion IV). However, there is no definitive link that all pens are not black either (Conclusion II).

Thus, we can deduce:
- Either Conclusion I (Some toys are black) or Conclusion III (No toy is black) must be true, but not both at the same time.
- Either Conclusion II (No pen is black) or Conclusion IV (Some pens are black) must be true, but not both simultaneously.

Therefore, the correct logical answer is: "Either I or III and either II or IV".