Difficulty: Easy
Correct Answer: Only (1) and (2)
Explanation:
Introduction / Context:
This verbal reasoning item tests classic categorical syllogism skills using set relations such as “All A are B”. The goal is to decide which conclusions must follow from the given statements, not which could be true.
Given Data / Assumptions:
Concept / Approach:
Chain rules: if all A are B and all B are C, then all A are C. Immediate inferences: from “All A are B”, we commonly accept “Some B are A” in these exam styles (existential import). Also, converse statements like “All C are B” generally do not follow.
Step-by-Step Solution:
From 1 and 2, derive: all green are white (green ⊆ blue ⊆ white). Test (1): “Some blue are green.” Since at least one green exists and every green is blue, some blue are indeed green. Conclusion (1) follows. Test (2): “Some white are green.” From green ⊆ white and existence of green, at least some white are green. Conclusion (2) follows. Test (3): “Some green are not white.” This contradicts green ⊆ white, so it does not follow. Test (4): “All white are blue.” This is the converse of statement 2 and is not implied. It may be false if some white are not blue.
Verification / Alternative check:
Think of circles: green inside blue, blue inside white. Visualizing confirms (1) and (2) must be true, while (3) and (4) need not be.
Why Other Options Are Wrong:
Options listing (3) are wrong since (3) contradicts the chain. Options listing (4) assume a converse which is not guaranteed. Hence only the option with (1) and (2) is valid.
Common Pitfalls:
Confusing “All B are C” with “All C are B” (converse error) and forgetting the typical exam convention that allows deriving a “Some …” statement from an “All …” statement given existence.
Final Answer:
Only (1) and (2)
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