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?

The correct option is: A, E and F are fighters.

Let us break down the relationships between the individuals step-by-step based on the rules of the society:
1. Coward and Coward: Always friends.
2. Fighter and Coward: Always enemies.
3. Fighter and Fighter: Always indifferent to one another.

From these rules, we can deduce the categories of relationships:
- If two people are friends, they must both be cowards (since fighters are indifferent, and fighter-coward pairs are enemies).
- If two people are indifferent, they must both be fighters (since cowards are friends, and fighter-coward pairs are enemies).
- If two people are enemies, one must be a fighter and the other must be a coward.

Now, let us analyze the given information:
- E and F are indifferent to each other: Since indifference only exists between two fighters, both E and F must be fighters.
- A and E are not enemies: We already established that E is a fighter. If A were a coward, A and E would have to be enemies. Since they are not enemies, A must also be a fighter.
- A and B are enemies: Since A is a fighter, B must be a coward (as fighter-coward pairs are enemies).
- C and D are friends: Since friendship only exists between two cowards, both C and D must be cowards.

Let us verify with the last condition:
- B and F are enemies: B is a coward and F is a fighter, which perfectly matches the rule that fighter-coward pairs are enemies.

Thus, we have determined the category of each person:
- Fighters: A, E, and F
- Cowards: B, C, and D

Comparing this to the options, the statement "A, E and F are fighters" is correct.