Two statements are given, followed by two conclusions numbered I and II. 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:
* All pineapples are papayas.
* All papayas are pears.
Conclusions:
* I. All pineapples are pears.
* II. Some pears are pineapples.
- ABoth conclusions I and II follow
- BNeither conclusion I nor II follows
- COnly conclusion II follows
- DOnly conclusion I follows
Solution & Step-by-step Explanation
Let's analyze the statements using set theory or Venn diagrams:
1. "All pineapples are papayas" means the set of Pineapples () is completely contained inside the set of Papayas (): .
2. "All papayas are pears" means the set of Papayas () is completely contained inside the set of Pears (): .
From these two, we can conclude that , which means all Pineapples are contained within Pears.
Evaluating Conclusions:
* Conclusion I: "All pineapples are pears" is true since . Thus, it follows.
* Conclusion II: "Some pears are pineapples" is also true because the region of pineapples is a part of the pears region. Thus, it follows.
Therefore, both conclusions I and II follow.
1. "All pineapples are papayas" means the set of Pineapples () is completely contained inside the set of Papayas (): .
2. "All papayas are pears" means the set of Papayas () is completely contained inside the set of Pears (): .
From these two, we can conclude that , which means all Pineapples are contained within Pears.
Evaluating Conclusions:
* Conclusion I: "All pineapples are pears" is true since . Thus, it follows.
* Conclusion II: "Some pears are pineapples" is also true because the region of pineapples is a part of the pears region. Thus, it follows.
Therefore, both conclusions I and II follow.