Statements: All roses are flowers. Some flowers are red. Conclusions: I. Some roses are red. II. No rose is red. Which follows?
Either I or II follows. Neither is certain on its own, but they are a complementary pair about the same two terms: one of 'some roses are red' and 'no rose is red' must be true. So the answer is 'either I or II'.
Explain it simply
Sometimes neither conclusion is certain, yet together they cover every possibility. Either at least one rose is red, or none is; there is no third option. Placement tests reward spotting this "either-or" case. It applies when the two conclusions share the same subject and predicate, one is a 'some' statement and the other a 'no' statement (or 'all' and 'some not'), and neither follows on its own.
Example
Statements: All roses are flowers. Some flowers are red.
- Roses are inside Flowers. Red things overlap Flowers somewhere, but possibly away from the roses.
- I (some roses are red): possible, not certain.
- II (no rose is red): possible, not certain.
- Same subject (roses), same predicate (red). One is 'some', the other is 'no'. They cannot both be false.
- Answer: either I or II follows.
Checklist for "either-or":
- Neither conclusion follows individually.
- Both talk about the same two terms.
- The pair is Some/No or All/Some-not.
Contrast: if II had been "All roses are red", the pair would be Some/All, which can both be false, so the answer would be "neither follows".
What to say in the interview
"Neither conclusion is forced by the statements, but they are about the same two terms, and 'some roses are red' and 'no rose is red' can't both be false. So either I or II follows."
Common mistakes
- Answering 'neither follows' without checking for a complementary pair.
- Marking either-or for pairs like Some/All, which can both be false.