Using arbitrage arguments explain why the price of an American call option on a stock paying no dividends should be the same as the price of a...

Using arbitrage arguments explain why the price of an American call option on a stock paying no dividends should be the same as the price of a corresponding European call. Why when the stock pays dividends the above argument can not be used. Give a numerical example (choosing x, k, r, T −t, σ) in which it is obvious (without any formulas) that American put price on a nondividend paying stock is larger then the corresponding European put price.