Identify the correct option regarding the given statements and conclusions:
Statements:
1. All swans are fishes.
2. All fishes are crabs.
Conclusions:
1. All swans are crabs.
2. Some crabs are swans.
- AOnly Conclusion 2 follows.
- BBoth Conclusions 1 and 2 follow.
- CNeither Conclusion 1 nor 2 follows.
- DOnly Conclusion 1 follows.
Solution & Step-by-step Explanation
From the statements, we can draw a Venn diagram relationships:
* Statement 1 implies .
* Statement 2 implies .
Combining them gives , which means all swans are inside the set of crabs.
* Conclusion 1 ("All swans are crabs") must be true.
* Conclusion 2 ("Some crabs are swans") must be true because the region belonging to swans is also part of crabs.
Thus, both conclusions follow.
* Statement 1 implies .
* Statement 2 implies .
Combining them gives , which means all swans are inside the set of crabs.
* Conclusion 1 ("All swans are crabs") must be true.
* Conclusion 2 ("Some crabs are swans") must be true because the region belonging to swans is also part of crabs.
Thus, both conclusions follow.