In the logical judgment questions of the Administrative Aptitude Test (AAT) in China’s civil service examinations, current problem-solving methods rely more on empirical summarization and question-sense training, aiming for speed and accuracy, but lacking rigorous logical proof. This article applies the theory of propositional logic in discrete mathematics, combined with the characteristics of recent AAT logical judgment questions, to analyze the correspondence between the stem expressions of the questions and the propositional logic structure. It provides a rigorous proof process for some logical judgment questions, offering a clear and verifiable theoretical basis for such problems.