All pens are red — Syllogisms Aptitude Question
All pens are red: Statements: All pens are red. No red thing is heavy. Conclusions: I. No pen is heavy. II. Answer and worked solution on CodeKairo.
- Topic: Syllogisms
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 75 seconds
Question
Statements:
- All pens are red.
- No red thing is heavy.
Conclusions: I. No pen is heavy. II. Some heavy things are pens.
Which conclusion follows?
Options
- Only I
- Only II
- Both
- Neither
Show the answer and the worked solution
Correct answer: A. Only I
Worked solution
- Pens ⊂ red, and red excludes heavy, so no pen is heavy: I follows.
- II contradicts that, so it cannot follow.
Answer: Only I.
The idea
When one conclusion is proved, any conclusion contradicting it is automatically false. That check is quicker than testing it separately.
Shortcut. All + no gives 'no pen is heavy'. A universal negative converts freely, so it equally says 'no heavy thing is a pen' — the exact denial of II, which therefore cannot follow.
Common trap. "Neither" — losing the thread in the double negative and doubting that pens inherit 'not heavy'; a subset shares every exclusion that applies to its superset.