All dogs are animals — Syllogisms Aptitude Question
All dogs are animals: Statements: All dogs are animals. All animals are living beings. Conclusions: I. Answer and worked solution on CodeKairo.
- Topic: Syllogisms
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 75 seconds
Question
Statements:
- All dogs are animals.
- All animals are living beings.
Conclusions: I. All dogs are living beings. II. Some living beings are dogs.
Which conclusion follows?
Options
- Only I
- Only II
- Both I and II
- Neither
Show the answer and the worked solution
Correct answer: C. Both I and II
Worked solution
- Dogs ⊂ animals ⊂ living beings, so every dog is a living being: I follows.
- Since dogs exist and all are living beings, some living beings are dogs: II also follows.
- Both conclusions hold.
Answer: Both I and II.
The idea
An 'all A are B' statement also supports 'some B are A', because the class A is taken to be non-empty. That converse is valid and often overlooked.
Shortcut. Two linked 'all' premises give 'All dogs are living beings' (I), and that conclusion converts to 'some living beings are dogs' (II).
Common trap. "Only I" — rejecting II as a reversed 'all' statement; the limited 'some' converse is valid because dogs exist.