Difficulty: Medium
Correct Answer: Only conclusion I follows.
Explanation:
Introduction / Context:
This question is a straightforward syllogism problem involving the sets fruits, leaves, and grapes. You are given one universal and one particular statement and asked to determine which conclusions are logically guaranteed. Such questions are common in competitive exams and test your ability to reason with set inclusion and partial overlap using simple Venn diagram ideas.
Given Data / Assumptions:
- Statement 1: All fruits are leaves. Every fruit lies inside the set of leaves.
- Statement 2: Some fruits are grapes. At least one fruit is also a grape.
- Conclusions refer to the relationships among leaves, grapes, and fruits.
- No other information about leaves or grapes is provided.
Concept / Approach:
The universal statement All fruits are leaves means that the fruit circle is completely within the leaf circle. The particular statement Some fruits are grapes means that there exists at least one element that is both a fruit and a grape. When evaluating conclusions, we look for what must always be true given these relationships. If a conclusion can be false in even one diagram that satisfies the statements, it does not logically follow.
Step-by-Step Solution:
Step 1: Draw a large circle representing leaves. Inside it, draw a smaller circle representing fruits, because all fruits are leaves.
Step 2: Now represent grapes. Since some fruits are grapes, we mark at least one region where the grape set intersects the fruit set. That region is therefore also inside the leaf set.
Step 3: Check Conclusion I: Some leaves are grapes. We have already identified at least one object that is both a fruit and a grape, and all fruits are leaves. Therefore, that object is also a leaf. This means there exists at least one leaf that is a grape. Hence Conclusion I definitely follows.
Step 4: Check Conclusion II: All grapes are fruits. The statements tell us only that some fruits are grapes, not that every grape must be a fruit. There may be grapes that are not fruits at all according to the given data, because nothing is said about grapes in general. Therefore, Conclusion II is not forced by the statements.
Step 5: Since only the first conclusion must hold in every valid configuration, the correct logical result is that only Conclusion I follows.
Verification / Alternative check:
Construct a quick example. Suppose all fruits are leaves, and apples, oranges, and grapes are types of fruits. Let us assume that two of the fruits are grapes, while there also exist some grapes that are not considered fruits in this simplified model. In such a case, the statements are satisfied: all fruits are leaves and some fruits are grapes. However, not all grapes are fruits, because some grapes fall outside the fruit category in this hypothetical setup. This confirms that Conclusion II is not guaranteed, while Conclusion I remains true since some leaves are indeed grapes.
Why Other Options Are Wrong:
- Any option that includes Conclusion II overstates the information given about grapes.
- The option stating that both conclusions follow is incorrect because we have shown a scenario where some grapes are not fruits.
- The options that reject both conclusions or say that nothing can be determined ignore the direct and clear implication behind Some fruits are grapes combined with All fruits are leaves.
Common Pitfalls:
Many candidates confuse some with all and assume symmetry where it does not exist. Another typical mistake is to think that if some fruits are grapes, then grapes and fruits must be identical sets. This is not logically valid. Always remember that some only guarantees partial overlap and that universal statements must be read exactly as given.
Final Answer:
Therefore, only the first conclusion is logically guaranteed by the statements, so the correct answer is Only conclusion I follows.
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