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Unformatted text preview: 2 Tuesday, July 10, 2007 10:04 AM Valid impossible for conclusion to be false if premises are true. We can test this by checking for counterexamples. A counterexample is one in the same logical for, but has true premises and a false conclusion. Fundamental principle of Logic if an argument is valid then any argument with the same form is valid. If an argument is invalid then any argument with the same form is invalid. Example: No cats are dogs T No dogs are apes T Valid? Same Form so example 1 is invalid. /No cats are apes T No men are women T No women are fathers T Invalid! / No men are fathers F Example All humans are mammals T No humans are reptiles T No mammals are reptiles T All men are human T No men are women T No humans are women F Chapter 2 Quantifiers All, some, none, every .... We've replaced the descriptive terms with formal terms so we do the same with the quantifiers. Connectives an expression that takes one or more statements as inputs and produces a single statement as output. _____ or_____ _____ if _____ _____AND ______ It is false that ________ If _____ then _______, otherwise _______ A statement not formed with connectives is an atomic/simple statement. A compound or molecular statement is formed of smaller statements. Truthvalues TRUE if statement is true and FALSE if statement is false. Truth functional connectives. A mathematical connective refers to a certain numerical function. Similarly a truth function operates on one or more truth values and returns a truth value. AND is a conjunction. F and F = F Intro to Logic Page 1 T and F = F T and T = T For a connective to be truth functional the truth value of the result must be directly determined by the truth value of the input. & And ~ Not V Or if, then if and only if Negation, Not, ~ 21 possibilities, T or F It is raining > it is not raining R T F ~R F T truth table Negation is truth functional. A T F ~A F T Conjunction, AND, & 22 possibilities, T&T, T&F, F&T, F&F True if and only if both statements are true A T T F F B T F T F A&B T F F F A T T F F & T F F F B T F T F Disjunction, OR, V Inclusive or, essentially and/or A T T F F B T F T F AVB T T T F A T T F F V T T T F B T F T F Intro to Logic Page 2 ...
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