All pens are blue — Syllogisms Aptitude Question
All pens are blue: Statements: All pens are blue. All blue things are attractive. Conclusions: I. Answer and worked solution on CodeKairo.
- Topic: Syllogisms
- Section: Logical Reasoning
- Difficulty: Easy
- Time target: 75 seconds
Question
Statements:
- All pens are blue.
- All blue things are attractive.
Conclusions: I. All pens are attractive. II. Some attractive things are pens.
Which conclusion follows?
Options
- Only I
- Only II
- Both
- Neither
Show the answer and the worked solution
Correct answer: C. Both
Worked solution
- Pens ⊂ blue ⊂ attractive, so all pens are attractive: I follows.
- Pens exist and are attractive, so some attractive things are pens: II follows.
Answer: Both.
The idea
Chain 'all' statements in one direction only. The 'some' converse of a valid 'all' conclusion is also valid.
Shortcut. All + all chains forwards to 'All pens are attractive', and that conclusion converts to 'some attractive things are pens'.
Common trap. "Only I" — rejecting II as a reversed 'all'; the limited 'some' converse of a valid 'all' conclusion always holds.