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 bananas are pears.
Some pears are grapes.
All grapes are sour.
Conclusions:
I. All bananas are grapes.
II. Some pears are sour.
III. Some bananas are grapes.
- AOnly conclusion I follows
- BOnly conclusion II follows
- COnly conclusion III follows
- DNone of the conclusions follows
Solution & Step-by-step Explanation
Let's analyze the conclusions with respect to the given statements:
Conclusion I & III: "All bananas are grapes" / "Some bananas are grapes"
There is no direct or definitive connection given between bananas and grapes. Thus, conclusions I and III do not logically follow.
Conclusion II: "Some pears are sour."
We know that "Some pears are grapes" and "All grapes are sour". The portion of pears that overlaps with grapes will definitely be sour. Therefore, Conclusion II logically follows.
Conclusion I & III: "All bananas are grapes" / "Some bananas are grapes"
There is no direct or definitive connection given between bananas and grapes. Thus, conclusions I and III do not logically follow.
Conclusion II: "Some pears are sour."
We know that "Some pears are grapes" and "All grapes are sour". The portion of pears that overlaps with grapes will definitely be sour. Therefore, Conclusion II logically follows.