When neither follows — Syllogisms Aptitude Question
When neither follows: Statements: Some pens are red. Some red things are expensive. Conclusions: I. Answer and worked solution on CodeKairo.
- Topic: Syllogisms
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 105 seconds
Question
Statements:
- Some pens are red.
- Some red things are expensive.
Conclusions: I. Some pens are expensive. II. No pen is expensive.
Which conclusion follows?
Options
- Only I
- Only II
- Either I or II
- Neither
Show the answer and the worked solution
Correct answer: C. Either I or II
Worked solution
- Two 'some' premises prove nothing definite, so neither holds on its own.
- Pens and expensive things must either overlap or not, and I and II are exactly those two cases.
- So either I or II holds.
Answer: Either I or II.
The idea
Whenever neither conclusion follows alone, check whether they form a complementary pair. If they do, the answer is 'either/or' rather than 'neither'.
Shortcut. Two 'some' premises prove nothing, so check the conclusions as a pair: 'some pens are expensive' and 'no pen is expensive' share both terms and contradict, so one must hold.
Common trap. "Neither" — correctly seeing that neither conclusion is proved on its own and stopping before noticing that I and II together cover every case.