Solution
= Solution
{c}
The terminal put payoff obeys $0\leq(K-S_T)^+\leq K$. If the put cost more than the <zero-coupon bond> paying $K$, sell the put and buy that bond. Invest the strictly positive initial difference in the bank account. At maturity the bond covers every possible put liability and the extra investment remains positive. This <arbitrage> is excluded, so
$$
\boxed{P(t,S_t)\leq Ke^{-r(T-t)}.}
$$