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

Let's break down the given statement into premises and then evaluate the options. Premises: 1. All good athletes want to win. (Good Athlete -> Wants to Win) 2. All athletes who want to win eat a well-balanced diet. (Wants to Win -> Eats Well-balanced Diet) From these two premises, we can chain them together: Good Athlete -> Wants to Win -> Eats Well-balanced Diet Therefore, a direct conclusion is: 3. All good athletes eat a well-balanced diet. (Good Athlete -> Eats Well-balanced Diet) Now let's evaluate each option based on this derived conclusion (3) and the original premises: A) no bad athlete wants to win This means "If an athlete is not good, they do not want to win." This is the inverse of Premise 1 (Good Athlete -> Wants to Win). The inverse is not necessarily true. A bad athlete might still want to win. So, A is incorrect. B) no athlete who does not eat a well-balanced diet is a good athlete This means "If an athlete does not eat a well-balanced diet, then they are not a good athlete." This is the contrapositive of our derived conclusion (3): "All good athletes eat a well-balanced diet." The contrapositive of a true statement is always true. If (Good Athlete -> Eats Well-balanced Diet), then its contrapositive (Not Eats Well-balanced Diet -> Not Good Athlete) is logically valid. So, B is correct. C) every athlete who eats a well-balanced diet is a good athlete This means "If an athlete eats a well-balanced diet, then they are a good athlete." This is the converse of our derived conclusion (3): "All good athletes eat a well-balanced diet." The converse is not necessarily true. Eating a well-balanced diet is a necessary condition for a good athlete (according to the premises), but not a sufficient one to define a good athlete. One could eat well but still be a poor performer. So, C is incorrect. D) all athletes who want to win are good athletes. This means "If an athlete wants to win, then they are a good athlete." This is the converse of Premise 1 (Good Athlete -> Wants to Win). The converse is not necessarily true. A bad athlete might still want to win. So, D is incorrect. The conclusion drawn in the original statement ("therefore all athletes who do not eat a well- balanced diet are bad athletes") is essentially the same as option B, assuming "bad athlete" means "not a good athlete." Option B is the only logically sound deduction from the given premises.