Final answer:
While extramarital relationships in ancient Rome were neither officially sanctioned nor nonexistent, societal and legal pressures likely made such relationships secretive and possibly brief, aligning closest with brief encounters with no commitment.
Step-by-step explanation:
In ancient Rome, extramarital relationships were not officially sanctioned by the state and often fell under social and legal scrutiny, especially in regard to women and the strict moral codes of pudicitia. Despite the Roman state's efforts to curb such relationships through laws like the Lex Julia de Adulteriis, extramarital affairs did occur. However, it is difficult to categorize them as either A. long lasting, B. sanctioned by the state, C. brief encounters with no commitment, or D. nonexistent, because the historical record suggests they could be of various natures, and societal attitudes towards them varied.
Nonetheless, societal pressure and the potential for severe consequences such as shaming, legal action, or even violence discouraged open extramarital relationships. Hence, it could be inferred that while extramarital relationships did exist, they often had to be conducted with a level of secrecy and were possibly brief due to the risks involved, aligning closest with the option C. brief encounters with no commitment.