Examining the Validity of Inference Rules: Utilizing Truth Tables and Contrapositive Analysis

In mathematical discrete logic, rules of inference play a fundamental role in reasoning and drawing valid conclusions. This paper focuses on proving the common rules of inference using truth tables for the contrapositive. The contrapositive is a powerful tool that allows for the examination of the logical relationships between conditional statements. By constructing truth tables for the contrapositive of each rule of inference, we can systematically evaluate the validity of the rules. The analysis involves assigning truth values to the premises and determining the truth values of the conclusions based on the contrapositive truth tables. The results demonstrate the consistency and soundness of the rules of inference, providing a rigorous foundation for logical reasoning in mathematical discrete logic. This approach showcases the applicability of truth tables and the contrapositive in establishing the validity of the rules of inference, thereby enhancing our understanding and utilization of logical principles in mathematical discrete logic.