Three statements are given, followed by three conclusions I, II and III. Considering the statements to be true, even if they seem to be at variance from commonly known facts, decide which conclusion(s) logically follows from the statements.
Statement :
All schools are colleges.
All colleges are houses.
All houses are roads.
Conclusion :
I. All schools are roads.
II. All schools are houses.
III. All colleges are roads.
- AOnly conclusions II and III follow.
- BOnly conclusion I and II follow.
- CAll conclusions follow.
- DOnly conclusion I and III follow.
Solution & Step-by-step Explanation
Let's analyze the statements sequentially:
All schools are colleges (Schools⊆Colleges)
All colleges are houses (Colleges⊆Houses)
All houses are roads (Houses⊆Roads)
From these implications, we can form a nested relationship chain:
Schools⊆Colleges⊆Houses⊆Roads
Now let's evaluate each conclusion:
Conclusion I: All schools are roads. Since Schools⊆Roads holds true from the chain, this conclusion follows.
Conclusion II: All schools are houses. Since Schools⊆Houses holds true from the chain, this conclusion follows.
Conclusion III: All colleges are roads. Since Colleges⊆Roads holds true from the chain, this conclusion follows.
Therefore, all conclusions follow.
All schools are colleges (Schools⊆Colleges)
All colleges are houses (Colleges⊆Houses)
All houses are roads (Houses⊆Roads)
From these implications, we can form a nested relationship chain:
Schools⊆Colleges⊆Houses⊆Roads
Now let's evaluate each conclusion:
Conclusion I: All schools are roads. Since Schools⊆Roads holds true from the chain, this conclusion follows.
Conclusion II: All schools are houses. Since Schools⊆Houses holds true from the chain, this conclusion follows.
Conclusion III: All colleges are roads. Since Colleges⊆Roads holds true from the chain, this conclusion follows.
Therefore, all conclusions follow.