Statements: 1. All A are B. 2. Some A are C. Conclusions: I. Some B are C. II. Some C are A. Which conclusion(s) logically follow? MCQ with Answer and Explanation
Statements:
1. All A are B.
2. Some A are C.
Conclusions:
I. Some B are C.
II. Some C are A.
Which conclusion(s) logically follow?
A. Only conclusion I follows
B. Neither I nor II follows
C. Only conclusion II follows
D. Both I and II follow
Answer: Option D
Solution (By JKExamLibrary)
Since some A are C, and all A are inside B, the intersection of A and C must also be inside B, meaning some B are C (I). 'Some A are C' directly implies its reverse 'Some C are A' (II). Both follow.
Explanation:
Smoking increases risk but doesn't guarantee cancer, so I does not follow. Teeth staining is a common effect, so II is possible and thus follows as a probable conclusion.
Statements:
1. All squares are rectangles.
2. All rectangles are polygons.
Conclusions:
I. All squares are polygons.
II. Some polygons are squares.
Which conclusion(s) logically follow?
Explanation:
A -> B and B -> C means A -> C. Therefore, all squares are polygons (Conclusion I). Since all squares are polygons, it implies that at least some polygons (those specific squares) are squares (Conclusion II).
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