Consider $A = \{1, 2, ..., 16\}$. A partition of $A$ into nonempty sets $A_1, A_2,..., A_n$ is said to be good if none of the Ai contains elements $a, b, c$ (not necessarily distinct) such that $a = b + c$. (a) Find a good partition $\{A_1, A_2, A_3, A_4\}$ of $A$. (b) Prove that no partition $\{A_1, A_2, A_3\}$ of $A$ is good