For options written on a non-dividend paying asset, which of the following is true?

I) An American put is intrinsically more valuable than the European put with the same maturity.

II) An American call is intrinsically more valuable than the European call with the same maturity

III) Decreasing the volatility of the underyling stock would increase the value of the European put but not that of a european call.

A) II Only

B) II AND III only

C) I only

D) None

E) I and III only