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 ----------------------
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 ----------------------
Statements:
I No athletes are vegetarians.
II All players are athletes.
III Therefore ----------------------
Show Hint
Take one player, push him into the athletes group, then see which group the first premise keeps him out of.
Updated On: Jul 17, 2026
- no players are vegetarians
- all players are vegetarian
- some players are vegetarian
- all vegetarians are players
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question.
Two premises are given and we must supply the conclusion that logically follows. The first premise is a universal negative, no athletes are vegetarians. The second is a universal affirmative, all players are athletes.
Step 2: Key Formula or Approach.
The middle term here is "athletes", since it appears in both premises and must vanish from the conclusion. The rule for combining a universal affirmative with a universal negative is that the conclusion is universal negative. In diagram terms, if one group sits wholly inside a second group, and the second group is wholly cut off from a third group, then the first group is wholly cut off from the third group as well.
Step 3: Detailed Explanation.
Premise II places the entire players circle inside the athletes circle.
Premise I places the athletes circle completely outside the vegetarians circle, with no overlap at all.
So every player, being an athlete, must lie in a region that has no contact with vegetarians. There is no way for a player to be a vegetarian without first being an athlete who is a vegetarian, and premise I forbids that.
The conclusion is therefore "No players are vegetarians", which is option (A).
Step 4: Checking the Wrong Options.
Option (B), all players are vegetarian, is the exact opposite of what the premises force. It would need players to sit inside the vegetarians circle, which is out of bounds.
Option (C), some players are vegetarian, is equally impossible. The overlap between players and vegetarians is empty, so not even one player can be a vegetarian.
Option (D), all vegetarians are players, tries to run the reasoning backwards. Vegetarians are only told to stay away from athletes. Nothing places them inside the players circle, and in fact the premises push them out of it.
Step 5: Final Answer.
No players are vegetarians, so the answer is (A).
Two premises are given and we must supply the conclusion that logically follows. The first premise is a universal negative, no athletes are vegetarians. The second is a universal affirmative, all players are athletes.
Step 2: Key Formula or Approach.
The middle term here is "athletes", since it appears in both premises and must vanish from the conclusion. The rule for combining a universal affirmative with a universal negative is that the conclusion is universal negative. In diagram terms, if one group sits wholly inside a second group, and the second group is wholly cut off from a third group, then the first group is wholly cut off from the third group as well.
Step 3: Detailed Explanation.
Premise II places the entire players circle inside the athletes circle.
Premise I places the athletes circle completely outside the vegetarians circle, with no overlap at all.
So every player, being an athlete, must lie in a region that has no contact with vegetarians. There is no way for a player to be a vegetarian without first being an athlete who is a vegetarian, and premise I forbids that.
The conclusion is therefore "No players are vegetarians", which is option (A).
Step 4: Checking the Wrong Options.
Option (B), all players are vegetarian, is the exact opposite of what the premises force. It would need players to sit inside the vegetarians circle, which is out of bounds.
Option (C), some players are vegetarian, is equally impossible. The overlap between players and vegetarians is empty, so not even one player can be a vegetarian.
Option (D), all vegetarians are players, tries to run the reasoning backwards. Vegetarians are only told to stay away from athletes. Nothing places them inside the players circle, and in fact the premises push them out of it.
Step 5: Final Answer.
No players are vegetarians, so the answer is (A).
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