midterm1Cribsheet - Truth Tables for Logical Operators P...

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Unformatted text preview: Truth Tables for Logical Operators P False False True True Q False True False True PQ False False False True P Q P Q PQ False True True True False True True False True True False True PQ True False False True False Rules of Inference P Fig 2.1, Hall/O'Donnell Discrete Mathematics with a Computer Springer, 2000 True Combinational Gate Symbols for Logical Operators with conventional and EE notation for operations ab a + = ab Some Theorems in Rule Form ab {Comm} ba And Commutes ab {Comm} ba Or Commutes More Theorems in Rule Form {DeMF} (a)(b) DeMorgan Or Fwd {noMiddle} a (a) Law of Excluded Middle (a b) (a)(b) {DeMB} (a b) DeMorgan Or Bkw ab bc {Chain} ac Implication Chain Rule (a b) {()Comm} (b a) Not Or Commutes ab b {modTol} a Modus Tollens ab {conPosF} (b)(a) Contrapositive Fwd (a b) {DeMF} (a)(b) DeMorgan And Fwd (a)(b) {DeMB} (a b) DeMorgan And Bkw a a {+&-} False NeverBoth ab {F} (a) b Implication Fwd (a) b {B} ab a b a {disjSyll} b Disjunctive Syllogism (a) { F} a a { B} (a) Double Negation Fwd Double Negation Bkw Implication Bkw Laws of Boolean Algebra page 1 Laws of Boolean Algebra From Fig 2.1, Hall & O'Donnell, Discrete Math with a Computer, Springer, 2000 page 2 From Fig 2.1, Hall & O'Donnell, Discrete Math with a Computer, Springer, 2000 Some theorems: (a b) b = b (a b) b = b (a b) c = (a c) (b c) { absorption} { absorption} { imp} ...
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This test prep was uploaded on 04/08/2008 for the course CS 2603 taught by Professor Rexpage during the Spring '08 term at The University of Oklahoma.

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