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 players are cricketers.
Some players are robots.
Conclusions:
I. Some cricketers are players.
II. Some cricketers are robots.
- AEither conclusion I or II follows.
- BOnly conclusion II follows.
- COnly conclusion I follows.
- DBoth conclusions I and II follow.
Solution & Step-by-step Explanation
Let's analyze using Venn diagrams or logical deduction:
Statement 1: All players are cricketers. This means the set of 'Players' is entirely inside the set of 'Cricketers'. Consequently, the intersection of cricketers and players is non-empty, so "Some cricketers are players" is definitely true. Thus, Conclusion I follows.
Statement 2: Some players are robots. Since all players are part of cricketers, the section of players that are robots must also be part of cricketers. Therefore, those robots are definitely cricketers. Thus, "Some cricketers are robots" is definitely true. Hence, Conclusion II follows.
Since both conclusions I and II follow logically, the correct option is D.
Statement 1: All players are cricketers. This means the set of 'Players' is entirely inside the set of 'Cricketers'. Consequently, the intersection of cricketers and players is non-empty, so "Some cricketers are players" is definitely true. Thus, Conclusion I follows.
Statement 2: Some players are robots. Since all players are part of cricketers, the section of players that are robots must also be part of cricketers. Therefore, those robots are definitely cricketers. Thus, "Some cricketers are robots" is definitely true. Hence, Conclusion II follows.
Since both conclusions I and II follow logically, the correct option is D.