A three-step chain — Syllogisms Aptitude Question
A three-step chain: Statements: All mangoes are fruits. All fruits are food. All food is perishable. Conclusions: I. Answer and worked solution on CodeKairo.
- Topic: Syllogisms
- Section: Logical Reasoning
- Difficulty: Medium
- Time target: 75 seconds
Question
Statements:
- All mangoes are fruits.
- All fruits are food.
- All food is perishable.
Conclusions: I. All mangoes are perishable. II. Some perishable things are mangoes.
Which conclusion follows?
Options
- Only I
- Only II
- Both
- Neither
Show the answer and the worked solution
Correct answer: C. Both
Worked solution
- Mangoes ⊂ fruits ⊂ food ⊂ perishable, so all mangoes are perishable: I follows.
- Mangoes exist and are perishable, so some perishable things are mangoes: II follows.
Answer: Both.
The idea
Chains of 'all' pass forwards through any number of links. The 'some' converse of a valid 'all' conclusion is also valid.
Shortcut. The all-chain gives 'All mangoes are perishable', and any valid 'all' conclusion converts to a 'some': some perishable things are mangoes.
Common trap. "Only I" — rejecting II as a reversed 'all' statement; the limited 'some' converse of a valid 'all' conclusion always holds.