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?

Here's a step-by-step deduction:

1. Analyze "C and D are friends": According to the rules, "Two cowards are always friends." This means C and D must both be cowards. (C = Coward, D = Coward)

2. Analyze "E and F are indifferent to each other": According to the rules, "Fighters are indifferent to one another." This means E and F must both be fighters. (E = Fighter, F = Fighter)

3. Analyze "B and F are enemies": We know F is a fighter. According to the rules, "A fighter and a coward are always enemies." Since F (fighter) and B are enemies, B must be a coward. (B = Coward)

4. Analyze "A and B are enemies": We know B is a coward. According to the rules, "A fighter and a coward are always enemies." Since A and B (coward) are enemies, A must be a fighter. (A = Fighter)

5. Verify "A and E are not enemies": We deduced A is a fighter and E is a fighter. "Fighters are indifferent to one another" means they are not enemies, which is consistent.

Summary of deductions: A = Fighter B = Coward C = Coward D = Coward E = Fighter F = Fighter

Now let's evaluate the options:

A) B, C and F are cowards: Incorrect. F is a fighter. B) A, E and F are fighters: Correct. A, E, and F are all fighters. C) B and E are in the same category: Incorrect. B is a coward, E is a fighter. D) A and F are in different categories: Incorrect. A is a fighter, F is a fighter (same category).

Therefore, statement B is correct.