In connection with studies of reliability of coherent binary systems, it has been suggested that a set of binary random variables be called associated if all pairs of binary nondecreasing functions of these variables have nonnegative covariance. In this note it is shown that there exists a unique smallest set A of pairs of binary nondecreasing functions on the variables such that nonnegative covariance for the pairs in A is necessary and sufficient condition for association of the variables. This set A is characterized and it is shown that its size increases rapidly with the number of variables. It is also shown that for four or more variables there exist pairs in A corresponding to coherent systems with no nontrivial modules, thus suggesting it is impossible to find an equivalent definition of association of binary random variables which makes material use of partitioning of the variables. (Author).