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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 and decide which conclusion(s) logically follow(s) from the given statements. Statements: No horses are mirrors. Some lizards are horses. Conclusions: (I) Some horses are not lizards. (II) Some lizards are not mirrors.
Neither conclusion (I) nor (II) follows
Both conclusions (I) and (II) follow
Only conclusion (II) follows
Only conclusion (I) follows
Only conclusion (II) follows
Convert statements to standard syllogism types (No H is M = E-type, Some L are H = I-type). Check cross-terms and Venn diagram overlaps without making unwarranted assumptions.
Convert statements to standard syllogism types (No H is M = E-type, Some L are H = I-type). Check cross-terms and Venn diagram overlaps without making unwarranted assumptions.
Analyze Statement 1
Statement 1: 'No horses are mirrors' means the set of Horses (H) and Mirrors (M) are completely disjoint (E-type proposition).
Analyze Statement 2
Statement 2: 'Some lizards are horses' means there is an intersection between Lizards (L) and Horses (H) (I-type proposition).
Evaluate Conclusion I
Conclusion I: 'Some horses are not lizards.' From 'Some lizards are horses', we know part of L is H, but H to L in reverse (Some H are not L) does not definitely follow without additional constraints. Thus, Conclusion I does not logically follow.
Evaluate Conclusion II
Conclusion II: 'Some lizards are not mirrors.' Since the lizards that are also horses (the overlapping region between L and H) cannot be mirrors (because No horses are mirrors), those specific lizards are definitely not mirrors. Thus, Conclusion II logically follows.
A: Only conclusion (I) follows is incorrect because conclusion I does not follow. B: Neither conclusion (I) nor (II) follows is incorrect because conclusion II is valid. D: Both conclusions (I) and (II) follow is incorrect because conclusion I is undetermined.
C is correct because only conclusion (II) logically follows from the given statements.
In syllogisms involving negative statements (No A is B), always test the intersection region with third sets to verify negative conclusions like 'Some C are not B'.
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