Final answer:
The statement in question is false because an open society is based on achieved status allowing for social mobility, while a closed society is based on ascribed status with little opportunity for change.
Step-by-step explanation:
The statement 'While an "open society" is based on ascribed status, a "closed society" is based primarily on achieved status.' is false. In sociological terms, an open society is one where individuals can change their social status through personal achievements such as education and employment.
Factors like wealth, income, and occupation often determine one's class, which is indicative of an open system that allows for social mobility. On the other hand, a closed society is characterized by little opportunity for movement within its social structure. Social standing in closed systems, such as caste and slavery systems, is typically based on ascribed status - the social status a person is assigned at birth or assumes involuntarily later in life.