Computer science and Logic are intricately linked to create a theoretical framework and practical technology applications. This paper further assimilates information from select literature between 2000–2023 to analyze Logic's applicability and development in computer science. Integrating formal Logic into the development of algorithms, artificial intelligence, hardware, and software subsystems increases computational capabilities and problem-solving efficiency. The methods include an all-round review of literature and analysis of advancements that range in fuzzy Logic and multivalued Logic to enhance the capacity of AI to handle uncertainty and optimize complex processes. Tremendous progress has been noted in logic-driven AI frameworks that increase accuracy and reliability in real-world applications. Challenges still need to be of higher interest to students, and teaching discrete mathematics is difficult. Much emphasis is placed on innovative means of teaching the subject under study. Pedagogies and the integration of new technologies in the quantum computing domain. This has impacts that are not limited only to the academic community, but their effects also lead to technological development, economic growth, and improvement in societal progress at large. To the extent that these challenges related to the issues above are addressed, logic-based systems will provide enhanced educational outcomes, robust frameworks for innovation, and expanded societal benefits.