Take the statements below to be true, even if they differ from known facts. Which of the conclusions follow logically from them?
Statements:
1. All violins are instruments.
2. Some toys are not instruments.
Conclusions:
I. Some instruments are not toys.
II. Some toys are not violins.
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. “Some X are not Y” cannot be read the other way round.
“All violins are instruments”: the circle of violins lies inside the circle of instruments
“Some toys are not instruments”: part of the toys lies outside the instruments; the rest of the toys may lie anywhere, even over all the instruments
Conclusion I: Some instruments are not toys. — Does not follow. The toys may cover all the instruments, as in the diagram; then every instrument is a toy.
Conclusion II: Some toys are not violins. — Follows. The toys that are not instruments cannot be violins, because every violin is an instrument.