Accept every statement below as true, whatever the real world says. Which of the conclusions must then be true?
Statements:
1. All artists are dancers.
2. All singers are dancers.
Conclusions:
I. Some artists are singers.
II. Some dancers are artists.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Only conclusion II follows
A conclusion follows only if it is true in every diagram that fits the statements; each class named in a statement is taken to have members.
“All artists are dancers”: the circle of artists lies inside the circle of dancers
“All singers are dancers”: the circle of singers also lies inside the circle of dancers; nothing is said about artists and singers
Conclusion I: Some artists are singers. — Does not follow. Both circles lie inside dancers, but they need not meet: in this diagram no artist is a singer.
Conclusion II: Some dancers are artists. — Follows. Every artist is a dancer, so the artists themselves are dancers who are artists.