10-LogicalEquiv

10-LogicalEquiv - Discussion #10 Chapter 1, Section 5 1/19...

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Unformatted text preview: Discussion #10 Chapter 1, Section 5 1/19 Discussion #10 Logical Equivalences Discussion #10 Chapter 1, Section 5 2/19 Topics Laws Duals Manipulations / simplifications Normal forms Definitions Algebraic manipulation Converting truth functions to logic expressions Discussion #10 Chapter 1, Section 5 3/19 Laws of , , and Excluded middle law Contradiction law P P T P P F Name Law Identity laws P F P P T P Domination laws P T T P F F Idempotent laws P P P P P P Double-negation law ( P) P Discussion #10 Chapter 1, Section 5 4/19 Commutative laws P Q Q P P Q Q P Name Law Associative laws (P Q) R P (Q R) (P Q) R P (Q R) Distributive laws (P Q) (P R) P (Q R) (P Q) (P R) P (Q R) De Morgans laws (P Q) P Q (P Q) P Q Absorption laws P (P Q) P P (P Q) P Discussion #10 Chapter 1, Section 5 5/19 Can prove all laws by truth tables T F T F T T T F T T F F T T T T F F F T T T T F F F T F F T T T Q P (P Q) Q P De Morgans law holds. Discussion #10 Chapter 1, Section 5 6/19 Absorption Laws Prove algebraically P (P Q) (P T) (P Q) identity P (T Q) distributive (factor) P T domination P identity P (P Q) P P (P Q) P Venn diagram proof P Q Discussion #10 Chapter 1, Section 5 7/19 Duals To create the dual of a logical expression 1) swap propositional constants T and F, and 2) swap connective operators and ....
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10-LogicalEquiv - Discussion #10 Chapter 1, Section 5 1/19...

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