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Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusion/s logically follow/s from the given statements. Statements: All plants are rocks. All rocks are lakes. No lake is a kite. Conclusions: (I) No rock is a kite. (II) At least some lakes are plants.
Only conclusion (I) follows.
Both conclusions (I) and (II) follow.
Neither conclusion (I) nor (II) follows.
Only conclusion (II) follows.
Both conclusions (I) and (II) follow.
Apply the transitive property: If all A are B and all B are C, then all A are C. Since No C is D, it follows that no B (and no A) can be D.
Apply the transitive property: If all A are B and all B are C, then all A are C. Since No C is D, it follows that no B (and no A) can be D.
Visualize the hierarchies
Given: (1) All plants are rocks, (2) All rocks are lakes. This creates a nested set: Plants are inside Rocks, and Rocks are inside Lakes (Plants < Rocks < Lakes).
Analyze Conclusion (I)
Statement (3) says 'No lake is a kite'. Since rocks are inside lakes, rocks cannot be kites. Thus, 'No rock is a kite' is true.
Analyze Conclusion (II)
Since all plants are rocks and all rocks are lakes, all plants are necessarily lakes. Therefore, 'At least some lakes are plants' is true (the part of lakes that are plants).
A: Incorrect because it overlooks the truth of conclusion (II); C: Incorrect because both conclusions are logically valid; D: Incorrect because conclusion (I) is also logically valid based on the transitive relationship.
B is correct because conclusion (I) is a direct consequence of the negative relationship between lakes and kites, and conclusion (II) is a direct consequence of the inclusion of plants within lakes.
In Syllogisms, always check for negative statements first; they act as a 'fence' that restricts the entire category nested within it.
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