A society consists of only two types of people — fighters and cowards. Two cowards are always friends. A fighter and a coward are always enemies. Fighters are indifferent to one another. If A and B are enemies, C and D are friends, E and F are indifferent to each other, A and E are not enemies, while B and F are enemies. Which of the following statements is correct ?
- (a) B, C and F are cowards.
- (b) A, E and F are fighters. ✓ UPSC's answer
- (c) B and E are in the same category.
- (d) A and F are in different categories.
Why the answer is (b)
• Since C and D are friends, and only two cowards are always friends, both C and D must be cowards.
• Since E and F are indifferent to each other, and only fighters are indifferent to one another, both E and F must be fighters.
• Since B and F are enemies, and F is a fighter, B must be a coward (as fighter-coward pairs are enemies).
• Since A and B are enemies, and B is a coward, A must be a fighter (as fighter-coward pairs are enemies).
• The condition 'A and E are not enemies' is consistent because A is a fighter and E is a fighter, and fighters are indifferent (not enemies) to each other.
• Therefore, A, E, and F are all fighters, making option (b) correct.
Why the other options are wrong
- (a) B, C and F are cowards.
- B and F are enemies, so they cannot both be cowards because cowards are always friends.
- (c) B and E are in the same category.
- B is a coward and E is a fighter, so they are in different categories.
- (d) A and F are in different categories.
- A is a fighter and F is a fighter, so they are in the same category.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.