Consider the following logical statements about plants, trees, and the colour green. Assume that both statements are true and then decide which of the given conclusions definitely follow. Statement 1: All plants are trees. Statement 2: No tree is green. Conclusions: I. Some plants are green. II. Those plants which are not trees are green.

Difficulty: Medium

Correct Answer: Neither Conclusion I nor Conclusion II follows.

Explanation:


Introduction / Context:
This question checks your understanding of categorical logic with universal statements and their implications. We have two strong statements about plants, trees, and the colour green. The challenge is to see what they force us to accept, and also what they do not say. In particular, we must avoid reading extra meaning into phrases like all and none, and we must be careful with apparently tricky phrases like plants which are not trees.


Given Data / Assumptions:
- Statement 1: All plants are trees. Every plant belongs to the set of trees. - Statement 2: No tree is green. The sets trees and green objects do not overlap at all. - There is no mention of any plant that is not a tree. - Conclusions I and II must be tested only against these statements.


Concept / Approach:
From the statement All plants are trees, we know the set of plants is fully inside the set of trees. From No tree is green, we know that no member of the tree set can be green. Consequently, no plant can be green, because every plant is a tree. However, the second conclusion talks about plants which are not trees, which is actually an empty group under the first statement. In standard reasoning questions, we usually do not draw specific conclusions about an empty set unless it is explicitly handled.


Step-by-Step Solution:
Step 1: Visualise a large circle representing trees. Inside this circle, draw a smaller circle representing plants, because all plants are trees. Step 2: Now represent green objects as a separate region that does not intersect the tree circle at all, because no tree is green. Step 3: Since every plant lies inside the tree set, and no tree is green, it is impossible for any plant to be green. So the statement some plants are green is false in every situation that respects the given statements. Step 4: Therefore Conclusion I, which asserts that some plants are green, cannot follow. It is actually the opposite of what the combined statements imply. Step 5: Now consider Conclusion II: those plants which are not trees are green. Under Statement 1 there are no plants that are not trees. The phrase plants which are not trees refers to an empty group. Standard exam style syllogism treats this as something about a non existent category, so we cannot assert from the statements that such non existent plants are green. Step 6: Since the data does not confirm any actual green plant, and the group in Conclusion II is empty, neither of the two conclusions is logically forced by the given statements.


Verification / Alternative check:
An alternative way is to rephrase the information verbally. If every plant is a tree and no tree is green, then every plant is also not green. This directly contradicts Conclusion I. For Conclusion II, we note that the first statement has already ruled out the existence of a plant that is not a tree. The conclusion tries to assign the colour green to a group that does not exist according to the statements. Hence, it cannot be treated as a valid logical consequence in this exam setting.


Why Other Options Are Wrong:
- Options that include Conclusion I ignore the combined effect of the two statements, which actually eliminate green plants. - Options that include Conclusion II treat the phrase plants which are not trees as if that group is real, even though Statement 1 excludes it. - The either or option is incorrect because neither conclusion is supported, and there is no exclusive choice between them. - The cannot be determined option is wrong, because the statements are strong enough to show that both conclusions fail to follow.


Common Pitfalls:
Students sometimes misread All plants are trees as All trees are plants, which is not correct. Another trap is to misinterpret No tree is green as No green thing is a tree and then assume it says something about all non tree plants, which do not even exist under the first statement. Always respect the exact direction of universal statements and inspect whether the category discussed in a conclusion actually exists according to the premises.


Final Answer:
Thus, neither of the two conclusions follows from the given statements, so the correct answer is Neither Conclusion I nor Conclusion II follows.

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