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Unformatted text preview: EECS 203, Winter 2007 Discrete Mathematics Lecture 4 Rules of Inference and G odels Theorems January 16 Reading: Rosen [1.5] January 16 Rules of Inference and Godels Theorems, Page 1 4.1 Review A model (or interpretation ) M for a first order logic L is a universe U together with an assignment of actual objects in U for each constant, variable, function, and predicate in L . We say that M satisfies , denoted by M , if M = True . A wff is said to be valid if it is satisfied by all models. Two wffs and are logically equivalent if is valid. The following wffs are valid. A wff obtained from a propositional tautology by replacing each propositional variable by a wff. ( x ) [ x t ], for all wff and variable x , where [ x t ] is with all free x replaced by a term t .  x , for all wff with no free x . ( x (  )) (( x ) ( x )), for all wffs , and variable x . January 16 Rules of Inference and Godels Theorems, Page 2 4.1 Review x x , x x ....
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 Winter '07
 YaoyunShi

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