Difficulty: Easy
Correct Answer: Only conclusion I follows.
Explanation:
Introduction / Context:
This question is another syllogism-type item. You are given two statements about the relationships between staplers, pins and markers, and you must decide which conclusions logically follow. This tests your ability to handle partial overlaps and subset relations among sets.
Given Data / Assumptions:
Concept / Approach:
The key is to follow the logical chain. If “some staplers are pins” and “all pins are markers,” the staplers that are pins must also be markers. That supports Conclusion I. For Conclusion II, we ask whether the information implies that every marker is a pin; in fact, we only know every pin is a marker, not the reverse. So we must carefully respect the direction of the “all” statement.
Step-by-Step Solution:
From Statement I, we know there is at least one object that is both a stapler and a pin.
From Statement II, we know that each and every pin is also a marker.
Take the staplers that are pins; by Statement II, those pins are markers.
Therefore, at least some staplers (those that are pins) are also markers.
Thus Conclusion I, “Some staplers are markers,” is logically valid.
Consider Conclusion II, “All markers are pins.”
We only know pins ⊂ markers (every pin is a marker), not that markers ⊂ pins. There may be markers which are not pins (for example, highlighters, whiteboard markers, etc.).
Since nothing in the statements forces every marker to be a pin, Conclusion II does not logically follow.
Verification / Alternative check:
You can draw simple Venn diagrams: place the set of pins entirely inside the set of markers, and mark a region where staplers overlap with pins. This automatically creates a region where staplers overlap with markers (justifying Conclusion I). At the same time, markers clearly extend beyond pins, so “all markers are pins” cannot be justified. Any model consistent with the statements will have Conclusion I true and Conclusion II not necessarily true.
Why Other Options Are Wrong:
Choosing only Conclusion II reverses the direction of the “all pins are markers” relationship. Choosing both conclusions incorrectly treats the converse of the set relation as true. Saying that neither conclusion follows ignores the straightforward transitivity that supports Conclusion I. The “cannot be determined which” option is for ambiguous situations, but here the logical status of each conclusion is clear.
Common Pitfalls:
A frequent error is to unconsciously reverse set relations: reading “all pins are markers” as if it also meant “all markers are pins”. In syllogism problems, always check the exact direction of “all” statements and avoid assuming that the converse is automatically true.
Final Answer:
Only the statement “Some staplers are markers” follows logically from the given statements. The correct option is Only conclusion I follows.
Discussion & Comments