AHSME 1962 Problem 27

Let $a @ b$ represent the operation on two numbers, $a$ and $b$, which selects the larger of the two numbers, with $a@a = a$. Let $a ! b$ represent the operator which selects the smaller of the two numbers, with $a ! a = a$. Which of the following three rules is (are) correct? $\textbf{(1)}\ a@b = b@a \textbf{(2)}\ a@(b@c) = (a@b)@c \textbf{(3)}\ a ! (b@c) = (a ! b) @ (a ! c)$

$\textbf{(A)}\ (1)\text{ only} \textbf{(B)}\ (2)\text{ only} \textbf{(C)}\ \text{(1) and (2) only}$ $\textbf{(D)}\ \text{(1) and (3) only} \textbf{(E)}\ \text{all three}$