Pedro goes either hunting or fishing every day. If it is snowing & windy then Pedro goes hunting. If it is sunny and not windy then Pedro goes fishing. Sometimes it can be snowing and sunny. Which of the following statements must be true:
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If it is not sunny and it is snowing then Pedro goes hunting.
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If it is windy and Pedro does not go hunting then it is not snowing.
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If it is windy and not sunny then Pedro goes hunting.
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If it is windy and sunny then Pedro goes hunting.
The rules are: (snowing ∧ windy) → hunting, and (sunny ∧ ¬windy) → fishing. Option B uses the contrapositive of the first rule: if ¬hunting, then ¬(snowing ∧ windy), which means if it's snowing then it's not windy (¬windy). Since we know it's windy, it must not be snowing. This is logically valid. Options A and D make unjustified assumptions. Option C doesn't follow from either rule.
To answer this question, let's go through each option to understand why it is correct or incorrect:
Option A) If it is not sunny and it is snowing then Pedro goes hunting. This statement is not necessarily true. According to the given conditions, if it is snowing and windy, Pedro goes hunting. However, it does not specify what Pedro does if it is not sunny and snowing. Pedro could either go hunting or fishing in this case, so this statement is not necessarily true.
Option B) If it is windy and Pedro does not go hunting then it is not snowing. This statement is correct. According to the given conditions, if it is snowing and windy, Pedro goes hunting. Therefore, if Pedro does not go hunting, it means it is not snowing. So, this statement must be true.
Option C) If it is windy and not sunny then Pedro goes hunting. This statement is not necessarily true. According to the given conditions, if it is sunny and not windy, Pedro goes fishing. However, it does not specify what Pedro does if it is windy and not sunny. Pedro could either go hunting or fishing in this case, so this statement is not necessarily true.
Option D) If it is windy and sunny then Pedro goes hunting. This statement is not necessarily true. According to the given conditions, if it is sunny and not windy, Pedro goes fishing. It does not specify what Pedro does if it is windy and sunny. Pedro could either go hunting or fishing in this case, so this statement is not necessarily true.
The correct answer is B. If it is windy and Pedro does not go hunting, then it is not snowing. This statement is correct because if it is snowing and windy, Pedro goes hunting. Therefore, if Pedro does not go hunting, it means it is not snowing.