The paper presents the results related to the definition and adoption of structures of opposition, built with set-theoretic measures, to evaluate emotional dynamics that arise during conversations on social media. Specifically, a graded hexagon of opposition is used to compare the emotional profiles of individuals involved in a dyadic conversation. Set-theoretic measures, based on fuzzy logic, are used to construct the hexagon whose analysis allows us to understand the tendency of the conversation toward empathy or lack of empathy. The results can be useful in the context of the current trend of social media sensing and, in particular, to support social media providers in receiving early warnings related to the analysis of emotional dynamics that could lead to or degenerate into information disorder. The results have been evaluated with conversations extracted from the Empathetic Dialogue dataset.