Trustworthy Artificial Intelligence (TAI) has become a major focus of both academic research and practical applications. However, the operationalization of TAI principles faces significant challenges due to conceptual ambiguities and a plurality of guidelines. This article explores a symbolic-based approach to TAI for ensuring compliance with ethical, legal, and technical requirements in AI systems. The symbolic methodology uses formal methods such as automated and interactive theorem proving to enable transparent, consistent, and adaptive decision-making processes. A case study on the automation of Spontaneous Breathing Trials (SBT) in Intensive Care Unit (ICU) illustrates the application of this approach, addressing critical challenges such as system reliability, explainability, and compliance with clinical standards. In addition, this article highlights the didactic implications of TAI research through an interdisciplinary seminar at the University of Bamberg. This program integrated theoretical exploration with hands-on learning, fostered critical interdisciplinary skills, and inspired further research.