Let's look at a call with an exercise price of $20, a maturity of three months and a risk-free rate of 5%. The present value of this future $20 is given here:
>>>x=20*exp(-0.05*3/12) >>>round(x,2) 19.75 >>>
In three months, what will be the wealth of our portfolio which consists of a call on the same stock plus $19.75 cash today? If the stock price is below $20, we don't exercise the call and keep the cash. If the stock price is above $20, we use our cash of $20 to exercise our call option to own the stock. Thus, our portfolio value will be the maximum of those two values: stock price in three months or $20, that is, max(s,20).
On the other hand, how about a portfolio with a stock plus a put option with an exercise price of $20? If the stock price falls by $20, we exercise the put option and get $20. If the stock price is above $20, we simply keep the stock. Thus, our portfolio value will be the maximum of those two...