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In the following question, two statements are followed by two conclusions. You have to assume the given statements to be true, even if they seem to be at variance with commonly known facts. Read both the conclusions and then decide which of the given conclusions logically follows from the statements.
Statements:
All chairs are wooden.
No wooden thing is cheap.
Conclusions:
I. No chair is cheap.
II. All cheap things are wooden.
Only conclusion II follows
Only conclusion I follows
Both conclusions I and II follow
Neither conclusion I nor II follows
Only conclusion I follows
Apply the transitive property: If A is in B and B is separated from C, then A is definitely separated from C.
Apply the transitive property: If A is in B and B is separated from C, then A is definitely separated from C.
Visualize the Statements
Let All chairs (C) be inside the circle of Wooden things (W). Let the circle of Cheap things (Ch) be completely separate from the circle of Wooden things (W).
Evaluate Conclusion I
Since all chairs are inside wooden things, and no wooden thing is cheap, chairs are also prevented from touching cheap things. Thus, No chair is cheap is True.
Evaluate Conclusion II
The statements do not imply that cheap things are wooden; in fact, the premise states they are separate. Thus, All cheap things are wooden is False.
A: Conclusion II is False as there is no link between cheap and wooden. C: Conclusion II is False, so C cannot be true. D: Conclusion I is definitely True, so D is incorrect.
B is correct because Conclusion I follows from the transitive relationship between chairs, wooden items, and cheap items, while Conclusion II is not supported by the premises.
In 'No A is B' type questions, always remember that the relationship is bidirectional: 'No A is B' is identical to 'No B is A'.
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