Three statements are followed by conclusions numbered I, II. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow/s from the given statement.
Statements:
All paints are houses.
All houses are wood.
Some streets are wood.
Conclusion (I): Some streets are houses.
Conclusion (II): All paints are wood.
Correct Answer :
Only conclusion (II) follows.
Solution :
The correct answer is Only conclusion (II) follows.
Step-by-step Analysis:
Let us analyze the given statements and check the logical validity of each conclusion step-by-step.
Given Statements:
1. All paints are houses.
2. All houses are wood.
3. Some streets are wood.
Evaluating Conclusion (I): "Some streets are houses."
From Statement 2 ("All houses are wood") and Statement 3 ("Some streets are wood"), we know that the category of 'streets' intersects with 'wood'. However, this intersection with 'wood' does not guarantee an overlap with the subset of 'houses' inside 'wood'. Therefore, Conclusion (I) does not logically follow.
Evaluating Conclusion (II): "All paints are wood."
From Statement 1, we know that all 'paints' are contained within 'houses' (Paints ⊆ Houses).
From Statement 2, we know that all 'houses' are contained within 'wood' (Houses ⊆ Wood).
By transitive logic, since all paints are inside houses and all houses are inside wood, all paints must also be inside wood (Paints ⊆ Wood). Therefore, Conclusion (II) definitely follows.
Thus, only conclusion (II) logically follows from the given statements.
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