Lecture2 - Discrete Mathematics Propositional Logic 2-2 Use...

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1 Introduction Propositional Logic Discrete Mathematics Andrei Bulatov Discrete Mathematics – Propositional Logic 2-2 Use of Logic In mathematics and rhetoric: s Give precise meaning to statements. s Distinguish between valid and invalid arguments. s Provide rules of `correct’ reasoning. Natural language can be very ambiguous `If you do your homework, then you’ll get to watch the game.’ `You do your homework, or you’ll fail the exam.’ = `If you don’t do your homework, then you’ll fail the exam.’ `If you don’t do your homework, then you will not get to watch . ..’ Discrete Mathematics – Propositional Logic 2-3 Use of Logic (cntd) In computing: s Derive new data / knowledge from existing facts s Design of computer circuits. s Construction of computer programs. s Verification of correctness of programs and circuit design. s Specification What the customer real y needed How the Programmer understood it What the customer got Discrete Mathematics – Propositional Logic 2-4 Statements (propositions) Propositional logic deals with statements and their truth values A statement is a declarative sentence that can be true or false Truth values are TRUTH ( T or 1 ) and FALSE ( F or 0 ). Examples: - 1 + 1 = 2 (statement, T) - The moon is made of cheese (statement, F) - Go home! (not statement, imperative) - What a beautiful garden! (not statement, exclamation) - Alice said, `What a beautiful garden!’ (statement, depends on Alice) - y + 1 = 2 (not statement, uncertain) - The God exists (statement, ?) Discrete Mathematics – Propositional Logic 2-5 Compound Statements We cannot decide the truth value of a primitive statement. This is not what logic does. Instead we combine primitive statements by means of
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This note was uploaded on 10/14/2011 for the course MACM 101 taught by Professor Pearce during the Spring '08 term at Simon Fraser.

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Lecture2 - Discrete Mathematics Propositional Logic 2-2 Use...

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