MathDB

27

Part of 1962 AMC 12/AHSME

Problems(1)

Binary Operator

Source:

3/3/2010
Let a@b a @ b represent the operation on two numbers, a a and b b, which selects the larger of the two numbers, with a@a \equal{} a. Let a!b a ! b represent the operator which selects the smaller of the two numbers, with a ! a \equal{} a. Which of the following three rules is (are) correct? (1)\ a@b \equal{} b@a \qquad (2)\ a@(b@c) \equal{} (a@b)@c \qquad (3)\ a ! (b@c) \equal{} (a ! b) @ (a ! c) <spanclass=′latex−bold′>(A)</span> (1) only<spanclass=′latex−bold′>(B)</span> (2) only<spanclass=′latex−bold′>(C)</span> (1) and (2) only<spanclass=′latex−bold′>(D)</span> (1) and (3) only<spanclass=′latex−bold′>(E)</span> all three <span class='latex-bold'>(A)</span>\ (1)\text{ only} \qquad <span class='latex-bold'>(B)</span>\ (2) \text{ only} \qquad <span class='latex-bold'>(C)</span>\ \text{(1) and (2) only} \qquad <span class='latex-bold'>(D)</span>\ \text{(1) and (3) only} \qquad <span class='latex-bold'>(E)</span>\ \text{all three}