Accept every statement below as true, whatever the real world says. Which of the conclusions must then be true?
Statements:
1. All girls are pretty.
2. No girl is a boy.
3. Some pretty are beautiful.
Conclusions:
I. Some pretty are not boys.
II. Some girls are beautiful.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only conclusion I 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 girls are pretty”: the circle of girls lies inside the circle of pretty
“No girl is a boy”: the circle of boys does not touch the circle of girls
“Some pretty are beautiful”: the circle of beautiful overlaps the circle of pretty; nothing is said about girls and beautiful
Conclusion I: Some pretty are not boys. — Follows. The girls are pretty and none of them is a boy, so the girls are pretty who are not boys.
Conclusion II: Some girls are beautiful. — Does not follow. The beautiful circle has to overlap only the pretty circle; it need not reach the girls, as in the diagram.