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Lecture2

# 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: square4 Give precise meaning to statements. square4 Distinguish between valid and invalid arguments. square4 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: square4 Derive new data / knowledge from existing facts square4 Design of computer circuits. square4 Construction of computer programs. square4 Verification of correctness of programs and circuit design. square4 Specification What the customer really 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.

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

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