Question Details

All good athletes want to win and all athletes who want to win eat a well-balanced diet; therefore all athletes who do not eat a well-balanced diet are bad athletes.


The best conclusion from this statement is that

Options

A

no bad athlete wants to win.

B

no athlete who does not eat well-balanced diet is a good athlete.

C

every athlete who eats a well-balanced diet is a good athlete.

D

all athletes who want to win are good athletes.

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Correct Answer :

Option B

no athlete who does not eat well-balanced diet is a good athlete.

Solution :

The correct option is: no athlete who does not eat well-balanced diet is a good athlete.

To understand why this is the best conclusion, we can break down the statements in the premise using formal logic:
1. "All good athletes want to win." Let us represent "good athlete" as G and "athlete who wants to win" as W. This statement translates to: GW (If an athlete is good, then they want to win).
2. "All athletes who want to win eat a well-balanced diet." Let "eats a well-balanced diet" be represented as D. This statement translates to: WD (If an athlete wants to win, then they eat a well-balanced diet).

By applying the transitive property of logical implication, we can chain these two statements together:
Since GW and WD, it logically follows that:
GD (All good athletes eat a well-balanced diet).

Now, let us find the contrapositive of this combined implication GD. The contrapositive of any conditional statement "If P, then Q" is "If not Q, then not P", which is logically equivalent to the original statement.
The contrapositive of GD is:
¬D¬G (If an athlete does not eat a well-balanced diet, then they are not a good athlete).

This statement directly translates to: "no athlete who does not eat a well-balanced diet is a good athlete." Therefore, this is the most logically sound conclusion that can be drawn from the premises.

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