While a significant amount of research has been devoted to exploring why university students struggle applying logic, limited work can be found on how students actually make sense of the notational and structural components used in association with logic. We adapt the theoretical framework of unitizing and reification, which have been effectively used to explain the types of integrated understanding required to make sense of symbols involved in numerical computation and algebraic manipulation, to investigate students' conceptualizations of truth tables and implication statements. We put forth a two-dimensional space consisting of two continua as a framework to analyse the degree to which students' thinking is compartmentalized or unified. Results indicate that students tend to treat the constituent pieces that make up these mechanisms independently without an understanding of each as a whole or an integrated view of the two together. This fragmented treatment is contrasted with the instructor's unified view of both truth tables and implication statements.