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 follow(s) from the statements.
Statements:
All figs are twigs.
Some twigs are trees.
Some ants are trees.
Conclusions:
I. Some ants are twigs.
II. Some trees are figs.
- AEither conclusion I or II follows
- BNeither conclusion I nor II follows
- COnly conclusion I follows
- DOnly conclusion II follows
Solution & Step-by-step Explanation
Let's analyze using a standard Venn diagram approach:
"All figs are twigs" → The entire circle of Figs is inside Twigs.
"Some twigs are trees" → There is an intersection between Twigs and Trees. However, this intersection does not necessarily have to overlap with Figs.
"Some ants are trees" → There is an intersection between Ants and Trees. This circle does not necessarily have to touch Twigs or Figs.
Let's examine the conclusions:
Conclusion I: "Some ants are twigs." → There is no definitive overlap required between Ants and Twigs based on the statements. Hence, it does not follow.
Conclusion II: "Some trees are figs." → While Trees intersect with Twigs, they don't necessarily have to intersect with Figs. Hence, it does not follow.
Therefore, Neither conclusion I nor II follows.
"All figs are twigs" → The entire circle of Figs is inside Twigs.
"Some twigs are trees" → There is an intersection between Twigs and Trees. However, this intersection does not necessarily have to overlap with Figs.
"Some ants are trees" → There is an intersection between Ants and Trees. This circle does not necessarily have to touch Twigs or Figs.
Let's examine the conclusions:
Conclusion I: "Some ants are twigs." → There is no definitive overlap required between Ants and Twigs based on the statements. Hence, it does not follow.
Conclusion II: "Some trees are figs." → While Trees intersect with Twigs, they don't necessarily have to intersect with Figs. Hence, it does not follow.
Therefore, Neither conclusion I nor II follows.