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The question stem containing the statements and conclusions is not visible in the provided images.
Only conclusion (I) follows.
Only conclusion (II) follows.
Both conclusions (I) and (II) follow.
Neither conclusion (I) nor (II) follows.
Only conclusion (II) follows.
Convert statements to Venn diagrams or positive/negative rules: All doors are gates (Door within Gate) and No door is a lock (Door and Lock are separate). Conclusion II (No lock is a door) is the direct converse of the negative statement. Conclusion I (Some locks are gates) is a possibility but not certain.
Convert statements to Venn diagrams or positive/negative rules: All doors are gates (Door within Gate) and No door is a lock (Door and Lock are separate). Conclusion II (No lock is a door) is the direct converse of the negative statement. Conclusion I (Some locks are gates) is a possibility but not certain.
Step 1: Analyze Statement 1
All doors are gates. This means the entire set of doors is enclosed within the set of gates.
Step 2: Analyze Statement 2
No door is a lock. This means there is no intersection between the set of doors and the set of locks.
Step 3: Evaluate Conclusion I
Some locks are gates. Since there is no positive information connecting locks and gates, this conclusion does not logically follow with certainty.
Step 4: Evaluate Conclusion II
No lock is a door. Given 'No door is a lock', its converse 'No lock is a door' is universally true and directly follows.
A: Only conclusion (I) follows is incorrect because locks and gates have no mandatory overlap. C: Both conclusions follow is incorrect because Conclusion I is not definite. D: Neither conclusion follows is incorrect because Conclusion II is definitely true.
B is correct because conclusion (II) directly follows as the converse of the given negative statement 'No door is a lock', while conclusion (I) is uncertain.
Always test negative categorical statements for direct converse validity (No A is B equals No B is A).
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