In this question, three 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 follows/follow from the statements.
Statements: I. Some bamboos are sticks.
II. All canes are sticks.
III. All canes are twigs.
Conclusions: I. Some bamboos are twigs.
II. Some twigs are sticks.
- ANeither conclusion I nor II follows
- BOnly conclusion I follows
- COnly conclusion II follows
- DBoth conclusions I and II follow
Solution & Step-by-step Explanation
Let us translate the given statements into a relational layout or Venn diagram configuration:
Some bamboos are sticks ⟹ There is an intersection between the circle for Bamboos and the circle for Sticks.
All canes are sticks ⟹ The circle for Canes lies completely inside the circle for Sticks.
All canes are twigs ⟹ The circle for Canes lies completely inside the circle for Twigs.
Now let us evaluate each conclusion:
Conclusion I: Some bamboos are twigs.
There is no direct relationship or definite overlap established between Bamboos and Twigs. It is possible, but not certain or mandatory. Thus, Conclusion I does not logically follow.
Conclusion II: Some twigs are sticks.
Since all canes are inside Sticks, and all canes are also inside Twigs, the intersection containing "Canes" is part of both "Sticks" and "Twigs". Therefore, there will always be an overlap between Twigs and Sticks. Thus, Conclusion II definitely follows.
Hence, Only conclusion II follows.
Some bamboos are sticks ⟹ There is an intersection between the circle for Bamboos and the circle for Sticks.
All canes are sticks ⟹ The circle for Canes lies completely inside the circle for Sticks.
All canes are twigs ⟹ The circle for Canes lies completely inside the circle for Twigs.
Now let us evaluate each conclusion:
Conclusion I: Some bamboos are twigs.
There is no direct relationship or definite overlap established between Bamboos and Twigs. It is possible, but not certain or mandatory. Thus, Conclusion I does not logically follow.
Conclusion II: Some twigs are sticks.
Since all canes are inside Sticks, and all canes are also inside Twigs, the intersection containing "Canes" is part of both "Sticks" and "Twigs". Therefore, there will always be an overlap between Twigs and Sticks. Thus, Conclusion II definitely follows.
Hence, Only conclusion II follows.