  Four functions counting the number of subsets of $\{1, 2, ..., n\}$ having
particular properties are defined by Nathanson and generalized by many authors.
They derive explicit formulas for all four functions. In this paper, we point
out that we need to compute only one of them as the others will follow as a
consequence. Moreover, our method is simpler and leads to more general results
than those in the literature.
