Rules of Inference
In logic and mathematics, rules of inference (also known as inference rules or transformation rules) are a set of logical forms that allow us to derive conclusions from premises. They provide a systematic way to build arguments and construct proofs. Key Concepts Premise: A statement assumed to be true. Conclusion: A statement derived from the premises using rules of inference. Valid Argument: An argument where the conclusion logically follows from the premises. Sound Argument: A valid argument where all the premises are true. Common Rules of Inference Here are some of the most common rules of inference: Modus Ponens (MP) : If P, then Q. P. Therefore, Q. Example: If it rains, then the ground gets wet. It is raining. Therefore, the ground is wet. Modus Tollens (MT) : If P, then Q. Not Q. Therefore, not P. Example: If it rains, then the ground gets wet. The ground is not wet. Therefore, it is not raining. Hypothetical Syllogism (HS) : If P, then Q. If Q, then R...