Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some wickets are carpets.
All carpets are helmets.
Conclusions:
I. All helmets are carpets.
II. All wickets are helmets.
- ANeither conclusion I nor II follows
- BOnly conclusion II follows
- COnly conclusion I follows
- DBoth conclusions I and II follow
Solution & Step-by-step Explanation
Let's analyze the connections using basic set logic or Venn diagrams:
"Some wickets are carpets" means there is an intersection between the set of wickets and the set of carpets.
"All carpets are helmets" means the entire set of carpets is contained within the set of helmets.
Now evaluate the conclusions:
Conclusion I: "All helmets are carpets." This is not necessarily true, as the set of helmets can be larger than the set of carpets. Only "Some helmets are carpets" can be definitively concluded. Thus, I does not follow.
Conclusion II: "All wickets are helmets." We only know that the part of wickets intersecting with carpets belongs to helmets. We cannot say all wickets are helmets. Thus, II does not follow.
Therefore, neither conclusion I nor II follows.
"Some wickets are carpets" means there is an intersection between the set of wickets and the set of carpets.
"All carpets are helmets" means the entire set of carpets is contained within the set of helmets.
Now evaluate the conclusions:
Conclusion I: "All helmets are carpets." This is not necessarily true, as the set of helmets can be larger than the set of carpets. Only "Some helmets are carpets" can be definitively concluded. Thus, I does not follow.
Conclusion II: "All wickets are helmets." We only know that the part of wickets intersecting with carpets belongs to helmets. We cannot say all wickets are helmets. Thus, II does not follow.
Therefore, neither conclusion I nor II follows.