MGF 1106 Lecture Notes - Syllogism, Contraposition, Euler Diagram

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Example of an argument: if the gators win, i"ll buy dinner. Therefore, the gators won: p = the gators win q = i bought dinner, argument form: p q q____ p, [(p q) q] p. Is an argument valid or invalid: make a truth table, ex. [(p q) q] p if it is a tautology- the argument is valid if it is not a tautology- the argument is invalid p. Laws that can prove if an argument is valid: law of detachment: P q p____ q: law of contraposition: P q q r_ p r: law of disjunctive syllogism: Laws that can prove an argument is a fallacy (invalid: fallacy of converse: P q q____ p: fallacy of inverse: Euler diagrams: all a"s are b"s, no a"s are b"s, some a"s are b"s, some a"s are not b"s. Euler diagram examples: all students take no-doze. You can make multiple diagrams, therefore the argument is invalid: all students take no-doze.

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