In each of the following questions two statements are given and these...
In each of the following questions two statements are given and these...
Given:
Statements:
1. Some actors are singers.
2. All the singers are dancers.
Conclusions:
1. Some actors are dancers.
2. No singer is an actor.
To determine:
Which conclusion logically follows from the given statements?
Solution:
To solve this question, we need to analyze the given statements and check if the conclusions can be logically derived from them.
Analysis:
From the first statement, "Some actors are singers," we can infer that there is an overlap between the sets of actors and singers. This means that there are actors who are also singers. However, we do not know the exact number or percentage of actors who are singers.
From the second statement, "All the singers are dancers," we can infer that every singer is also a dancer. This means that there is no singer who is not a dancer. However, we do not know if there are any dancers who are not singers.
Conclusion 1: Some actors are dancers.
This conclusion can be logically derived from the given statements. Since some actors are singers and all singers are dancers, it is possible that some actors are also dancers. Therefore, conclusion 1 follows.
Conclusion 2: No singer is an actor.
This conclusion cannot be logically derived from the given statements. The first statement tells us that some actors are singers, which means there is an overlap between the sets of actors and singers. Therefore, it is possible for there to be singers who are also actors. Hence, conclusion 2 does not follow.
Final Answer:
Only conclusion 1, "Some actors are dancers," logically follows from the given statements. Therefore, the correct answer is option (A) Only (1) conclusion follows.