The concept of "logic" underpins both human cognition and computational processes, yet the mechanisms, strengths, and inherent limitations of common day-to-day human logic and computer logic diverge significantly. While computers are engineered for formal, explicit operations, excelling in speed and precision, human logic is characterized by its remarkable adaptability, intuitive processing, and an innate capacity to navigate ambiguity. This report aims to delineate these core differences, provide illustrative examples, and explore the profound implications of these distinctions, particularly within the evolving landscape of Artificial Intelligence (AI) and Human-Computer Interaction (HCI). Understanding this fundamental divergence is crucial for advancing AI systems and fostering effective collaboration between human and machine intelligence.