Analyze the statements below and determine which of the conclusions logically follows, assuming the statements to be absolutely true even if they contradict reality.
Statements:Correct Answer :
If only conclusion I follows
Solution :
The correct answer is: If only conclusion I follows.
Let us lay out the three given statements clearly before evaluating each conclusion:
Statement 1: Some Violins are Instruments
Statement 2: No Piano is a Violin
Statement 3: 0% of Instruments are Brass (i.e., No Instrument is a Brass)
Evaluating Conclusion I: "Some Violins can be Brass"
This is a possibility conclusion — it uses the word "can be," not "are." This is a crucial distinction in syllogism reasoning.
From Statement 1, only some Violins are Instruments — not all of them. This means there exists a portion of Violins that are not Instruments.
From Statement 3, no Instrument can be Brass. This restriction applies only to those Violins that happen to also be Instruments.
However, the Violins that fall outside the Instrument category are unrestricted by Statement 3. There is no rule in any of the three statements that prevents a non-Instrument Violin from being Brass.
Since there is a subset of Violins (the non-Instrument ones) for which the possibility of being Brass is not ruled out, Conclusion I — that some Violins can be Brass — is a valid possibility conclusion. ✔
Evaluating Conclusion II: "No Brass is a Piano"
To draw this conclusion, we would need a logical chain connecting Brass to Piano. Let us try to find one:
- Statement 2 tells us: No Piano is a Violin.
- Statement 3 tells us: No Instrument is a Brass.
- Statement 1 tells us: Some Violins are Instruments.
None of these statements establish any relationship — direct or indirect — between Brass and Piano. We cannot determine whether a Piano can or cannot be Brass based on the given information alone.
Since the relationship between Brass and Piano is completely undefined in the given statements, Conclusion II does NOT follow. ✗
Final Verdict:
✔ Conclusion I follows (as a valid possibility).
✗ Conclusion II does not follow (no logical link between Brass and Piano).
Therefore, the answer is: If only conclusion I follows.
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