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Propositional Logic - University at Buffalo

Propositional LogicCSE 191, Class Note 01 Propositional LogicComputer Sci & Eng DeptSUNY Buffaloc Xin He ( University at Buffalo )CSE 191 Discrete Structures1 / 37 Discrete MathematicsWhat isDiscrete Mathematics?In Math 141-142, you learn continuous math. It deals withcontinuous functions, differential and integral contrast, discrete math deals with mathematical topics in asense that it analyzes data whose values are separated (such asintegers: integer number line has gaps).Here is a very rough comparison between continuous math anddiscrete math: consider an analog clock (one with hands thatcontinuously rotate, which shows time in continuous fashion) vs. adigital clock (which shows time in discrete fashion).c Xin He ( University at Buffalo )CSE 191 Discrete Structures3 / 37 Course TopicsThis course provides some of the mathematical foundations and skillsthat you will need in your further study of computer science andengineering. These topics include: Logic ( Propositional and predicate Logic )Logical inferences and mathematical proofCounting methodsSets and set operationsFunctions and sequencesIntroduction to number theory and CryptosystemMathematical inductionRelationsIntroduction to graph theoryBy definition, computers operate on discrete data (binary strings).

The Foundations: Logic and Proof The rules of logic specify the precise meanings of mathematical statements. It is the basis of the correct mathematical arguments, that is, the proofs. It also has important applications in computer science: to verify that computer programs produce the correct output for all possible input values.

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