Discrete Math - Week 2
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This 2 page Class Notes was uploaded by Aaron Maynard on Tuesday February 2, 2016. The Class Notes belongs to CS 2305 at a university taught by Timothy Farage in Spring 2016. Since its upload, it has received 85 views.
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Eugh...this class is soo hard! I'm so glad that you'll be posting notes for this class
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Date Created: 02/02/16
Discreet Math for Computing AarothMastard Timothy Farage January 19 -21 , 2016 Compound Proposition Definition: Using multiple propositions with apparition. P -> (Q V R) P Q R ( Q V R ) P -> ( Q V R ) 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 If every circumstance is true, then the compound proposition is known as an example of "Tautology" A logical expression that is true for any values of its variables is said to be tautology. ( P Λ Q ) Λ (P -> Q) P Q PΛQ P->Q (PΛQ) Λ (P- >Q) 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 0 1 0 A compound proposition that is false for all values of its variables is known as a "contradiction". “I am that I am." Discreet Math for Computing AarothMastard Timothy Farage January 19 -21 , 2016 Math Equivalences: For any x and y, x + y = y + x x + 2 = 5 Logical Equivalences (Propositional Equivalences): PVQ QVP PΛQ QΛP (PVQ)VR PV(QVR) PΛ(QVR) (PΛQ)V(PΛR) ~P is known as “not P” Negate and Simplify: Definition: Simplifying until there are no negations except over variables. ~[(PΛQ) -> (Q->R)] (PΛQ) Λ ~(Q->R) (PΛQ) Λ (QΛ~R) PΛQΛ~R Done! Converse of P -> Q If the animal is a cat, then it has four legs. Q -> P If the animal has four legs, then it is a cat. If a triangle has 2 equal sides, then it has 2 equal angles. If a triangle has 2 equal angles, then it has 2 equal sides. Contrapositive of P -> Q If you get over 90%, then you get an A. ~P -> ~Q If you get an A, then you get over 90%. Things to have memorized: P->Q <=> ~PVQ ~(P->Q) <=> P Λ ~Q - The negation of an implication is NOT an implication, it's an AND! Demorgans Laws: ~(PVQ) <=> ~P Λ ~Q ~(P Λ Q) <=> ~PV~Q
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