• 1.3: Modus Ponens and Modus Tollens

    • A proof, or an argument, is a series of statements where each statement logically follows from the previous one(s). Logically follows means that there is a logic rule of inference that derives it from the previous statement(s). One famous rule of inference is modus ponens, which we will study in the next subunits.

    • Wikipedia: "List of Rules of Inference" URL

      Read over the text from Wikipedia on rules of inference. Rules of inference are used to show that one statement is a consequence of another statement and, thus, are used for constructing proofs. The summary table is located before the truth table and the examples. The Rules of Inference are referred to by names in the 3rd column in the table. In this course, alternate names are also used. Those that have corresponding alternate names are listed in the following table:

       Wikipedia Name

       Alternate Name

       Disjunction

       Generalization

       Conjunction

       Specialization

       Elimination

       Generalization

       Modus Ponens

      		  

       Modus Tollens

      		  

       Hypothetical Syllogism

       Transitivity

       Disjunctive Syllogism

       Disjunctive Elimination

       Resolution

       Elimination
    • Massachusetts Institute of Technology: Srini Devadas and Eric Lehman's "Proofs" URL

      Read Section 1, "The Axiomatic Method," up to Section 3 on pages 3 - 7. Please note that reading Section 3 on pages 7 - 9 is optional.

    • University of California, San Diego: Edward Bender and S. Williamson's "Arithmetic, Logic, and Numbers: Logic" URL

      Review example 4 (Right Triangles and the Pythagorean theorem) on pages Lo-6 - Lo-7. It illustrates some of the rules of inference.

    • Modus Ponens and Other Types of Reasoning URL

      Read this summary of Modus Ponens and other types of reasoning.