The price of a call option on a non-dividend paying stock is $4. The stock price is $31, the strike price is $30, and the expiration date is in three months. The risk-free interest rate is 8%.

a) If the option is European, compute the price of a European put on the same stock with the same strike price and expiration date.

b) If the option is American, derive the upper and lower bounds for the price of an American put on the same stock with the same strike price and expiration date.