Question

Instructions (133 to 135): Select the statement which logically follows the two given statements.

Statements:
I No athletes are vegetarians.
II All players are athletes.
III Therefore ----------------------

• A. no players are vegetarians
• B. all players are vegetarian
• C. some players are vegetarian
• D. all vegetarians are players

Hint:

Take one player, push him into the athletes group, then see which group the first premise keeps him out of.

Answer 1

The Correct Option is A

Handle this by tracing one individual rather than by drawing circles. Pick any person and call him a player. Premise II says every player is an athlete, so this person is an athlete. Premise I says no athlete is a vegetarian, so this person is not a vegetarian. The person was chosen at random from the players, so the same reasoning applies to each and every player.

1. no players are vegetarians: This is exactly what the trace produced. Any player you pick is pushed into the athletes group by the second premise and then pushed out of the vegetarians group by the first. Since the choice of player was arbitrary, the result holds for all of them.
2. all players are vegetarian: The trace shows the opposite for every single player, so this option contradicts both premises at once. It is the strongest possible wrong answer.
3. some players are vegetarian: This needs just one player to be a vegetarian. The trace blocks even that one, because the block applies to every player without exception. Weakening the claim from all to some does not rescue it.
4. all vegetarians are players: This reverses the direction of the argument. The premises only tell vegetarians where they cannot be, which is inside the athletes group and so inside the players group too. Being told where you cannot be never tells anyone where they must be.

A side note worth keeping. Since players sit inside athletes and athletes sit away from vegetarians, we can also say no vegetarians are players, which is just the same conclusion read from the other end. That is a legitimate restatement, unlike option (D) which claims something entirely different.

Let's summarize:

• Every player is an athlete, and no athlete is a vegetarian.
• So no player can be a vegetarian, and the exclusion covers all of them.
• A universal negative premise plus a universal affirmative premise gives a universal negative conclusion.

The conclusion that follows is option (A).