Difficulty: Medium
Correct Answer: Both I and II follow.
Explanation:
Introduction / Context:
This syllogism question links flowers with leaves and plants. Two statements are provided, one universal and one particular. Your task is to decide whether each of the two conclusions follows logically. This type of problem is very common in logical reasoning sections of competitive exams and is best approached using simple set diagrams and careful reading of the statements.
Given Data / Assumptions:
- Statement 1: All flowers are leaves. Every flower belongs to the leaf set.
- Statement 2: Some flowers are plants. At least one flower is also a plant.
- Flowers clearly exist because Statement 2 talks about some flowers.
- Conclusions I and II must be checked with only this information.
Concept / Approach:
The universal statement makes flowers a subset of leaves. The particular statement establishes an overlap between flowers and plants. Combining these, we can often derive overlaps between leaves and plants. In general, if all A are B and some A are C, then those some A are both B and C, so some B are C and some C are A. This pattern directly applies here. We just need to confirm it with a step by step analysis.
Step-by-Step Solution:
Step 1: From Statement 1, draw the flower circle completely inside the leaf circle. This means every flower is also a leaf.
Step 2: From Statement 2, mark an overlap between flowers and plants. There is at least one object that is both flower and plant.
Step 3: Since every flower is a leaf, the flower plant object is also a leaf. Therefore there is at least one object that is both a leaf and a plant. This directly supports Conclusion I: some leaves are plants.
Step 4: The same element also shows that some plants are flowers, because it is both plant and flower. This directly supports Conclusion II.
Step 5: Both conclusions are tied to the existence of that common element connecting flowers, leaves, and plants and are therefore logically guaranteed.
Verification / Alternative check:
For an intuitive check, imagine that roses, lilies, and marigolds are flowers. Suppose all flowers are classified as leaves in this abstract model. Also assume that some flowers, say roses, are plants. Then roses are simultaneously flowers, leaves, and plants. This shows that some leaves are plants and that some plants are flowers. Any other elements in the sets will not change these overlaps as long as the original statements remain true.
Why Other Options Are Wrong:
- Options that accept only one of the conclusions ignore the symmetry created by the common element that is both flower and plant.
- The option that rejects both conclusions contradicts the direct consequence of the subset relation combined with the some type overlap.
- The cannot be determined option is incorrect because we have clear evidence for both conclusions from the given statements alone.
Common Pitfalls:
A frequent error is to treat some as vague and think that almost nothing can be deduced from it. In truth, some gives very useful information about overlap. Another mistake is to ignore the subset relation and consider flowers, leaves, and plants as unrelated. Always start by putting all given statements into a consistent diagram and then read the conclusions from that picture.
Final Answer:
Thus, both conclusions definitely follow from the given statements, so the correct answer is Both I and II follow.
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