Theorems in propositional logic | Rules of inference | Classical logic

Modus ponens

In propositional logic, modus ponens (/ˈmoʊdəs ˈpoʊnɛnz/; MP), also known as modus ponendo ponens (Latin for "method of putting by placing") or implication elimination or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "P implies Q. P is true. Therefore Q must also be true." Modus ponens is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms such as affirming the consequent, denying the antecedent, and evidence of absence. Constructive dilemma is the disjunctive version of modus ponens. Hypothetical syllogism is closely related to modus ponens and sometimes thought of as "double modus ponens." The history of modus ponens goes back to antiquity. The first to explicitly describe the argument form modus ponens was Theophrastus. It, along with modus tollens, is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal. (Wikipedia).

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Modulus of a product is the product of moduli

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From playlist Intro to Complex Numbers

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Number Theory | Primitive Roots modulo n: Definition and Examples

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From playlist Primitive Roots Modulo n

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From playlist Introduction to Complex Numbers

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For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai Associate Professor Percy Liang Associate Professor of Computer Science and Statistics (courtesy) https://profiles.stanford.edu/percy-liang Assistant Professor

From playlist Stanford CS221: Artificial Intelligence: Principles and Techniques | Autumn 2021

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For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai Associate Professor Percy Liang Associate Professor of Computer Science and Statistics (courtesy) https://profiles.stanford.edu/percy-liang Assistant Professor

From playlist Stanford CS221: Artificial Intelligence: Principles and Techniques | Autumn 2021

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Logic 5 - Propositional Modus Ponens | Stanford CS221: AI (Autumn 2021)

For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai Associate Professor Percy Liang Associate Professor of Computer Science and Statistics (courtesy) https://profiles.stanford.edu/percy-liang Assistant Professor

From playlist Stanford CS221: Artificial Intelligence: Principles and Techniques | Autumn 2021

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For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai Associate Professor Percy Liang Associate Professor of Computer Science and Statistics (courtesy) https://profiles.stanford.edu/percy-liang Assistant Professor

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Related pages

Soundness | Law of total probability | Subjective logic | Function application | Lattice (order) | Hypothetical syllogism | Propositional calculus | Logical consequence | Denying the antecedent | Metalogic | Modus tollens | | Logical disjunction | Sequent calculus | Material conditional | Consequent | Antecedent (logic) | Sequent | Alfred Tarski | Deontic logic | Curry–Howard correspondence | Artificial intelligence | Argument | Proposition | Conditional probability | Affirming the consequent | Truth table | Constructive dilemma | Forward chaining | Formal proof | Admissible rule | Validity (logic) | Thomas Hobbes | Algebraic semantics (mathematical logic) | Rule of inference | Cut-elimination theorem | Formal system | Bertrand Russell | Alfred North Whitehead | Classical logic | Deductive reasoning | Boolean algebra (structure)