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 conclusion logically follow(s) from the statements.
Statements:
All threads are needles.
Some needles are brushes.
All needles are cupboards.
Conclusions:
I. Some brushes are cupboards.
II. All threads are cupboards.
III. All brushes are threads.
- AAll conclusions follow
- BOnly conclusions II and III follow
- COnly conclusions I and II follow
- DOnly conclusions I and III follow
Solution & Step-by-step Explanation
Let's analyze the connections using Venn sets:
All threads are needles → The set of Threads is entirely inside the set of Needles.
Some needles are brushes → The set of Needles intersects with the set of Brushes.
All needles are cupboards → The entire set of Needles is contained within the set of Cupboards.
Evaluating the conclusions:
Conclusion I: Some brushes are cupboards. Since all needles are inside cupboards, and some brushes intersect with needles, that intersecting region of brushes must also be inside cupboards. Thus, Conclusion I definitely follows.
Conclusion II: All threads are cupboards. Since all threads are inside needles, and all needles are inside cupboards, all threads must be inside cupboards. Thus, Conclusion II definitely follows.
Conclusion III: All brushes are threads. There is no definitive statement forcing all brushes to be inside threads. Thus, Conclusion III does not follow.
Hence, only conclusions I and II follow.
All threads are needles → The set of Threads is entirely inside the set of Needles.
Some needles are brushes → The set of Needles intersects with the set of Brushes.
All needles are cupboards → The entire set of Needles is contained within the set of Cupboards.
Evaluating the conclusions:
Conclusion I: Some brushes are cupboards. Since all needles are inside cupboards, and some brushes intersect with needles, that intersecting region of brushes must also be inside cupboards. Thus, Conclusion I definitely follows.
Conclusion II: All threads are cupboards. Since all threads are inside needles, and all needles are inside cupboards, all threads must be inside cupboards. Thus, Conclusion II definitely follows.
Conclusion III: All brushes are threads. There is no definitive statement forcing all brushes to be inside threads. Thus, Conclusion III does not follow.
Hence, only conclusions I and II follow.