Given below are three statements 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 of the conclusions logically follow(s) from the statements.
Statement :
All tanks are plates.
All cots are plates.
Some oats are cots.
Conclusion:
I. Some tanks are cots.
II. Some plates are tanks.
III. Some plates are oats.
- AOnly conclusion I follows
- BEither conclusion I follows or II follows
- COnly conclusion II follows
- DBoth conclusions II and III follow
Solution & Step-by-step Explanation
Let's analyze the statements:
Tanks⊆Plates
Cots⊆Plates
Oats∩Cots
=∅
Let's evaluate the conclusions:
Conclusion I: "Some tanks are cots." Tanks and cots are both inside plates, but they don't necessarily overlap with each other. This does not follow.
Conclusion II: "Some plates are tanks." Since All tanks are plates (Tanks⊆Plates), any element in the Tank set is also in the Plate set. Therefore, there are definitely some plates that are tanks. This follows.
Conclusion III: "Some plates are oats." Since All cots are plates and Some oats are cots, the overlapping region between oats and cots must lie inside plates. Therefore, those oats are also plates. This follows.
Hence, both conclusions II and III follow.
Tanks⊆Plates
Cots⊆Plates
Oats∩Cots
=∅
Let's evaluate the conclusions:
Conclusion I: "Some tanks are cots." Tanks and cots are both inside plates, but they don't necessarily overlap with each other. This does not follow.
Conclusion II: "Some plates are tanks." Since All tanks are plates (Tanks⊆Plates), any element in the Tank set is also in the Plate set. Therefore, there are definitely some plates that are tanks. This follows.
Conclusion III: "Some plates are oats." Since All cots are plates and Some oats are cots, the overlapping region between oats and cots must lie inside plates. Therefore, those oats are also plates. This follows.
Hence, both conclusions II and III follow.