Two classes inside a third — Syllogisms Aptitude Question
Two classes inside a third: Statements: All cats are animals. All dogs are animals. Conclusions: I. Answer and worked solution on CodeKairo.
- Topic: Syllogisms
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 105 seconds
Question
Statements:
- All cats are animals.
- All dogs are animals.
Conclusions: I. Some cats are dogs. II. No cat is a dog.
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
- Cats and dogs both sit inside animals, but the statements say nothing about their overlap.
- Neither conclusion is proved on its own.
- They are contradictory and exhaust every case, so either I or II holds.
Answer: Either I or II.
The idea
When two conclusions are contradictory and between them cover all possibilities, the answer is 'either/or'. Look for that pair whenever neither follows alone.
Shortcut. Same subject and predicate, one 'some' and one 'no' — I and II are a complementary pair, so exactly one is true. Once neither is proved alone, the answer is Either I or II without drawing a diagram.
Common trap. "Neither" — correctly seeing that neither conclusion is proved and stopping there, missing that 'some cats are dogs' and 'no cat is a dog' cannot both be false.