Identify the correct option regarding the Statements and Conclusions given:
Statements:
I. Some pumpkins are beetroots.
II. All beetroots are garlic.
III. All garlic are turnips.
Conclusions:
I. Some pumpkins are garlic.
II. All garlic are pumpkins.
III. All beetroots are turnips.
- AAll Conclusions follow.
- BOnly Conclusion I follows.
- COnly Conclusions I and III follow.
- DOnly Conclusions I and II follow.
Solution & Step-by-step Explanation
Let's analyze the conclusions using Venn diagrams:
* From statement I and II: Since some pumpkins are beetroots and all beetroots are garlic, that overlapping portion of pumpkins is also garlic. Hence, "Some pumpkins are garlic" (Conclusion I) definitely follows.
* From statement II and III: Since all beetroots are garlic and all garlic are turnips, then by transitivity, all beetroots are turnips. Hence, Conclusion III definitely follows.
* Conclusion II states "All garlic are pumpkins", which is not a mandatory condition.
Thus, only Conclusions I and III follow.
* From statement I and II: Since some pumpkins are beetroots and all beetroots are garlic, that overlapping portion of pumpkins is also garlic. Hence, "Some pumpkins are garlic" (Conclusion I) definitely follows.
* From statement II and III: Since all beetroots are garlic and all garlic are turnips, then by transitivity, all beetroots are turnips. Hence, Conclusion III definitely follows.
* Conclusion II states "All garlic are pumpkins", which is not a mandatory condition.
Thus, only Conclusions I and III follow.