1962 AMC 12 Question 27

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