Question: Suppose A, B, and C are statements such that C is true if exactly one of A and B is true. If C is false, which of the following statements must be true?
A: If A is true, then B is false.
B: If A is false, then B is false.
C: If A is false, then B is true.
D: Both A and B are true.
Please eliminate two incorrect options first, then think it step by step and choose the most proper one option.