You are given two statements and four conclusions. Choose the comment about…
2019
You are given two statements and four conclusions. Choose the comment about
conclusions from the options given below:
Statements:
All dancers are girls.
All girls are intelligent.
Conclusions:
I. Some girls are dancers.
II. No girl is dancer.
III. Some intelligent are dancers.
IV. All intelligent are dancers.
- A.
Only conclusions I and II follow
- B.
Only conclusions I and III follow
- C.
Only conclusion I follows
- D.
Only conclusion IV follows
Attempted by 172 students.
Show answer & explanation
Correct answer: B
Given statements: All dancers are girls. All girls are intelligent.
Dancers are a subset of girls (every dancer is a girl).
Girls are a subset of intelligent people (every girl is intelligent).
By transitivity, dancers are a subset of intelligent people (every dancer is intelligent).
Evaluation of the conclusions:
Conclusion I (Some girls are dancers): Follows. Since dancers are contained within girls, any dancer (if present) is a girl, so there are girls who are dancers.
Conclusion II (No girl is dancer): Does not follow. This contradicts the relation that dancers are girls and thus cannot be concluded.
Conclusion III (Some intelligent are dancers): Follows. Because dancers are intelligent (via girls), any dancer is an intelligent person, so some intelligent people are dancers.
Conclusion IV (All intelligent are dancers): Does not follow. The premises only assert that dancers are intelligent, not that every intelligent person is a dancer.
Final conclusion: Only the statements 'Some girls are dancers' and 'Some intelligent are dancers' follow from the given premises.