Three statements are given, followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
No chart is a casket.
Not a single casket is a house.
Every house is an adapter.
Conclusions:
(I) Some adapters which are houses are charts as well.
(II) No chart is a house.
(III) Some adapters are houses.
- ABoth conclusions II and III follow
- BOnly conclusion III follows
- CEither conclusion I or II follows
- DAll conclusions follow
Solution & Step-by-step Explanation
Let's systematically analyze each statement and conclusion:
Statement 3: "Every house is an adapter" means all houses are enclosed within adapters. This naturally guarantees that the intersecting zone between adapters and houses is non-empty. Hence, Conclusion III ("Some adapters are houses") definitely follows.
Statement 1 & 2: "No chart is a casket" and "No casket is a house". Since caskets do not overlap with charts or houses, there is no direct connection given between charts and houses. They can overlap or stay completely separated.
Therefore, Conclusion I ("Some adapters which are houses are charts as well") cannot be definitively true.
Conclusion II ("No chart is a house") is also not guaranteed to be true.
Hence, only conclusion III follows.
Statement 3: "Every house is an adapter" means all houses are enclosed within adapters. This naturally guarantees that the intersecting zone between adapters and houses is non-empty. Hence, Conclusion III ("Some adapters are houses") definitely follows.
Statement 1 & 2: "No chart is a casket" and "No casket is a house". Since caskets do not overlap with charts or houses, there is no direct connection given between charts and houses. They can overlap or stay completely separated.
Therefore, Conclusion I ("Some adapters which are houses are charts as well") cannot be definitively true.
Conclusion II ("No chart is a house") is also not guaranteed to be true.
Hence, only conclusion III follows.