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midterm1Cribsheet

# midterm1Cribsheet - Truth Tables for Logical Operators P...

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Truth Tables for Logical Operators P Q P Q False False False False True False True False False True True True P Q False True True True P Q False True True False P Q True True False True P Q True False False True ¬ P True False Combinational Gate Symbols for Logical Operators with conventional and EE notation for operations + ab a ¬ = ab Rules of Inference Fig 2.1, Hall/O’Donnell Discrete Mathematics with a Computer Springer, 2000 Some Theorems in Rule Form a ¬ a ⎯⎯⎯⎯ { +&- } False NeverBoth ¬ (a b) ⎯⎯⎯⎯⎯ { ¬ ( ) Comm } ¬ (b a) Not Or Commutes a b ¬ b ⎯⎯⎯⎯⎯⎯⎯ { modTol } ¬ a Modus Tollens a b ⎯⎯⎯ { Comm } b a Or Commutes a b ⎯⎯⎯ { Comm } b a And Commutes a b b c ⎯⎯⎯⎯⎯⎯ { Chain } a c Implication Chain Rule ⎯⎯⎯⎯⎯ { noMiddle } a ( ¬ a) Law of Excluded Middle a b ⎯⎯⎯⎯⎯ { conPos F } ( ¬ b) ( ¬ a) Contrapositive Fwd ( ¬ a) b ⎯⎯⎯⎯ { B } a b Implication Bkw a b ⎯⎯⎯⎯ { F } ( ¬ a) b Implication Fwd More Theorems in Rule Form ¬ (a b) ⎯⎯⎯⎯⎯
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