In this statement and conclusion question about dawn, day, and night, two statements are given. You must take the statements as true and decide which of the conclusions I and II logically follow. Statement 1: All dawn is day. Statement 2: No day is night. Conclusion I: No night is day. Conclusion II: Some dawn is night.

Difficulty: Easy

Correct Answer: Only conclusion I follows

Explanation:


Introduction / Context:
This question uses everyday time related words dawn, day, and night in a purely logical setting. The aim is to determine which conclusions about their relationships must follow from the given statements. Even though you might have intuitive ideas about how dawn, day, and night relate in real life, you must base your reasoning strictly on the logical content of the statements.


Given Data / Assumptions:
- Statement 1: All dawn is day, meaning the set representing dawn lies entirely inside the set representing day.
- Statement 2: No day is night, meaning the sets day and night are completely disjoint.
- Conclusion I: No night is day, which is the converse of Statement 2 but logically equivalent in this context.
- Conclusion II: Some dawn is night, claiming that dawn and night have at least one common element.


Concept / Approach:
We treat the terms as sets: Dd for dawn, D for day, and N for night. From Statement 1 we get Dd ⊆ D. From Statement 2 we get D ∩ N = empty set. Two things follow: anything that is dawn is also day, and nothing that is day can be night. We then check each conclusion. Conclusion I restates the non overlap between day and night from the perspective of night, while Conclusion II claims an overlap between dawn and night that appears to contradict the earlier information.


Step-by-Step Solution:
Step 1: Because all dawn is day, if an element belongs to Dd, it automatically belongs to D. Step 2: Statement 2 says that no element can belong to both D and N. So D and N are disjoint sets. Step 3: Conclusion I, "No night is day," is a symmetric restatement of Statement 2. If no day is night, then no night is day because the intersection of D and N is empty from both sides. Step 4: Therefore, Conclusion I follows directly and is logically valid. Step 5: Now check Conclusion II, "Some dawn is night." Any dawn element is also in D because Dd ⊆ D. Step 6: Since D and N have no common element, it is impossible for a dawn element, which is within D, to also be in N. Step 7: Therefore, the intersection of dawn and night must be empty, and Conclusion II is false.


Verification / Alternative check:
Draw D as a large circle, N as another circle that does not overlap D at all, and Dd as a smaller circle entirely inside D. Because D and N do not intersect, no part of Dd can intersect N. This diagram clearly supports Conclusion I and directly contradicts Conclusion II. There is no way to draw the sets differently without breaking the original statements, which confirms our evaluation.


Why Other Options Are Wrong:
Option B says only Conclusion II follows, but Conclusion II cannot possibly be true given that day and night do not overlap. Option C claims both conclusions follow, which would require dawn to overlap night even though dawn is inside day and day does not intersect night. Option D says neither follows, which ignores the fact that Conclusion I is logically equivalent to Statement 2. Option E suggests a mutually exclusive situation where exactly one of the two follows but does not identify which; the precise correct option is that only Conclusion I follows, which is given by Option A.


Common Pitfalls:
One common mistake is to rely too much on real life images of dawn being a transition between night and day, and then assume some overlap with night. However, the statements in this problem define dawn as completely contained within day, and they separate day entirely from night. Logical questions often redefine familiar words in ways that do not match real life, so always follow the given statements, not your intuition.


Final Answer:
The correct option is Only conclusion I follows, because "No night is day" is logically equivalent to "No day is night," while any overlap between dawn and night is directly ruled out by the given statements.

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