Consider an American and a European put option written on the same non-dividend-paying stock, with same maturity T and same strike price K. Remember that the values of an American and a European call option written on the same non-dividend-paying stock are equal, and we arrived to that conclusion in 4 steps. Your task is to try to prove similar steps for put options, and confirm 3 steps and show why 1 step fails. Use proof by contradiction. The 4 steps are: 1. ptAmpt 2. pt=ct+PVt(K)St 3. ct+PVt(K)StPVt(K)St 4. PVt(K)St>KSt