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The wording "maximal subset of S" is mistaken. "Maximal" does not mean largest. It means any set that can't be extended by adding a new element of S without violating the definition of the desired subset (the non-divisibility property). The correct term is "maximum", which means largest. Again, "maximal" only means not extendible, and a maximal subset may not be a maximum subset.
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Non-Divisible Subset
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The wording "maximal subset of S" is mistaken. "Maximal" does not mean largest. It means any set that can't be extended by adding a new element of S without violating the definition of the desired subset (the non-divisibility property). The correct term is "maximum", which means largest. Again, "maximal" only means not extendible, and a maximal subset may not be a maximum subset.