All A are B, no B is C — Syllogisms Aptitude Question
All A are B, no B is C: Statements: All students are hardworking. No hardworking person is lazy. Conclusions: I. Answer and worked solution on CodeKairo.
- Topic: Syllogisms
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 90 seconds
Question
Statements:
- All students are hardworking.
- No hardworking person is lazy.
Conclusions: I. No student is lazy. II. Some hardworking people are students.
Which conclusion follows?
Options
- Only I
- Only II
- Both
- Neither
Show the answer and the worked solution
Correct answer: C. Both
Worked solution
- Students ⊂ hardworking, and hardworking excludes lazy entirely, so no student is lazy: I follows.
- Students exist and are all hardworking, so some hardworking people are students: II follows.
Answer: Both.
The idea
'All A are B' plus 'no B is C' gives the strong conclusion 'no A is C'. That combination is one of the few that supports a universal negative.
Shortcut. 'All A are B' + 'No B is C' is the pattern that yields a universal 'No A is C' (I), and statement 1 converts to 'some hardworking people are students' (II).
Common trap. "Only I" — rejecting II as a reversal of 'all students are hardworking'; the limited 'some' converse is valid because students exist.