Difficulty: Medium
Correct Answer: Only conclusion I follows.
Explanation:
Introduction / Context:
This question involves three time related sets: dawn, day, and night. The statements tell us how these sets relate to each other, and the conclusions test your understanding of negative universal relationships. You must decide which conclusion follows necessarily if both statements are accepted as logically true, without bringing in your own knowledge about real world time periods.
Given Data / Assumptions:
- Statement 1: All dawn is day. The set dawn is entirely inside the set day.
- Statement 2: No day is night. There is no overlap between day and night.
- The existence of dawn and day is assumed in the context of the problem.
- Conclusions I and II must be checked strictly against these statements.
Concept / Approach:
The statement No day is night tells us that the sets day and night do not intersect. In logic, the statement No A is B is equivalent to No B is A. Hence, from No day is night, we can also say No night is day. The first conclusion captures this direct equivalence. The first statement All dawn is day puts dawn entirely inside day, and because day does not intersect night, dawn also cannot intersect night. This will help us test the second conclusion that claims some dawn is night.
Step-by-Step Solution:
Step 1: Visualise the set day and the set night as two disjoint circles, because No day is night.
Step 2: Place the set dawn as a smaller circle completely inside the day circle, because All dawn is day.
Step 3: Examine Conclusion I: No night is day. If no element of day is night, then there is no element that belongs to both day and night. The relationship is symmetric, so night and day do not overlap in either direction. Thus No night is day is equivalent to No day is night and definitely follows.
Step 4: Examine Conclusion II: Some dawn is night. Since all dawn is inside day and day has no overlap with night, dawn also has no overlap with night. Therefore, it is impossible for any part of dawn to be night. The conclusion that some dawn is night contradicts the given statements.
Step 5: Because Conclusion I is a valid restatement of the second statement and Conclusion II contradicts the set diagram, only the first conclusion follows.
Verification / Alternative check:
To verify, imagine marking points on a time line. Let the period labelled day have no intersection with the period labelled night, in line with Statement 2. Place dawn strictly within the day period. In such an arrangement, it is immediately clear that nothing in night can be day and nothing in dawn can be night. This confirms that the first conclusion is correct while the second is impossible under the given premises.
Why Other Options Are Wrong:
- Any option that accepts Conclusion II fails to respect the fact that day and night are disjoint sets.
- The option claiming both conclusions are true is wrong because the second conclusion contradicts the set relations.
- The option that rejects both conclusions ignores the direct equivalence between No day is night and No night is day.
- The cannot be determined option is incorrect because the statements are strong enough to decide the status of both conclusions.
Common Pitfalls:
Some students misinterpret No A is B as only one directional and hesitate to accept the reverse No B is A. Others try to use real life intuition about dawn, day, and night, rather than treating the terms as abstract sets. In exam style logical reasoning, you must rely only on the structural relationships stated in the problem and not on your personal understanding of time or nature.
Final Answer:
Therefore, only the first conclusion is logically supported, so the correct answer is Only conclusion I follows.
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