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: Some fish are limes.
All limes are chairs.
Some chairs are big.
Conclusions: I. Some limes are big.
II. Some fish are chairs.
III. All limes are fish.
- ANone of the conclusions follows
- BOnly conclusion III follows
- COnly conclusion I follows
- DOnly conclusion II follows
Solution & Step-by-step Explanation
Let's analyze the conclusions with standard overlapping sets:
Conclusion I: Some limes are big.
We know all limes are chairs and some chairs are big, but the 'big' circle might not intersect with 'limes'. This is possible but not definite. Hence, it does not follow.
Conclusion II: Some fish are chairs.
We are given that 'Some fish are limes' and 'All limes are chairs'. Since all limes are inside the chair set, the fish that are limes must also be chairs. Therefore, this conclusion definitely follows.
Conclusion III: All limes are fish.
We only know 'Some fish are limes'. This does not mean all limes are fish. Hence, it does not follow.
Thus, only conclusion II follows.
Conclusion I: Some limes are big.
We know all limes are chairs and some chairs are big, but the 'big' circle might not intersect with 'limes'. This is possible but not definite. Hence, it does not follow.
Conclusion II: Some fish are chairs.
We are given that 'Some fish are limes' and 'All limes are chairs'. Since all limes are inside the chair set, the fish that are limes must also be chairs. Therefore, this conclusion definitely follows.
Conclusion III: All limes are fish.
We only know 'Some fish are limes'. This does not mean all limes are fish. Hence, it does not follow.
Thus, only conclusion II follows.