Step-by-step Solution:

By definition, the symmetric difference is \( A \Delta B = (A \setminus B) \cup (B \setminus A) \). When we intersect with \( C \), we get \( (A \Delta B) \cap C = ((A \setminus B) \cap C) \cup ((B \setminus A) \cap C) \), which matches option B. Option A expands to the same set since intersection distributes over symmetric difference. Option D is \( ((A \cup B) \setminus (A \cap B)) \cap C \), which is also another form of the symmetric difference intersected with \( C \). Option C evaluates to \( C \setminus (A \cap B) \), which is not necessarily equal to \( (A \Delta B) \cap C \). Thus, option C is the correct answer.