Which of the Following Statements Is False

Which of the following statements is false?

A) For a call written on a stock with a positive beta, the beta of the call always exceeds the beta of the stock.
B) The beta of a put option written on a negative beta stock is always negative.
C) As the stock price changes, the beta of an option will change, with its magnitude falling as the option goes in-the-money.
D) A put option is a hedge, so its price goes up when the stock price goes down.