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: All footballs are hockey sticks.
All hockey sticks are stumps.
No stump is a ring.
Conclusions: I. Some stumps are footballs.
II. No hockey stick is a ring.
III. Some footballs are rings.
- AOnly conclusions I and III follow.
- BAll conclusions I, II and III follow.
- COnly conclusions II and III follow.
- DOnly conclusions I and II follow.
Solution & Step-by-step Explanation
Let's analyze using Venn diagrams:
All footballs are inside hockey sticks.
All hockey sticks are inside stumps. Thus, all footballs are also inside stumps.
No stump is a ring. This means the ring circle is completely separated from stumps, hockey sticks, and footballs.
Let's check the conclusions:
Conclusion I: Some stumps are footballs. (True, because all footballs are stumps).
Conclusion II: No hockey stick is a ring. (True, because hockey sticks are inside stumps, and no stump is a ring).
Conclusion III: Some footballs are rings. (False, as there is no overlap possible between footballs and rings).
Therefore, only conclusions I and II follow.
All footballs are inside hockey sticks.
All hockey sticks are inside stumps. Thus, all footballs are also inside stumps.
No stump is a ring. This means the ring circle is completely separated from stumps, hockey sticks, and footballs.
Let's check the conclusions:
Conclusion I: Some stumps are footballs. (True, because all footballs are stumps).
Conclusion II: No hockey stick is a ring. (True, because hockey sticks are inside stumps, and no stump is a ring).
Conclusion III: Some footballs are rings. (False, as there is no overlap possible between footballs and rings).
Therefore, only conclusions I and II follow.