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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.
 Spring '08
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