Are the phrases skill set and skill sets both correct?
As I see it, set implies a single set of related skills whereas sets can be taken to mean multiple sets of skills around different concentrations.
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In reference to all of one's skills, the term 'skill set' includes all of a person's skills with none left out of the fold or on the sidelines. But if we wanted to convey a breakdown of skills into different areas and components, the term 'multiple' can be used to more clearly convey a plurality of sets, as in 'multiple skill sets'. In this instance, 'sets' is plural.