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
Correct Answer :
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 and "athlete who wants to win" as . This statement translates to: (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 . This statement translates to: (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 and , it logically follows that:
(All good athletes eat a well-balanced diet).
Now, let us find the contrapositive of this combined implication . 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 is:
(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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