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A role set is anyone you have a recurring relationship with in your role. According to Goffman the "role set" is the various kinds of relevant audiences for a particular role. Merton describes "role set" as the "complement of social relationships in which persons are involved because they occupy a particular social status." For instance, the role of a doctor has a role set comprising colleagues, nurses, patients, hospital administrators, etc.
The term "role set" was coined by Robert K. Merton in 1957. He made a clear distinction between a "role set" and a "status set".
References
Role set Wikipedia(Text) CC BY-SA