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# lect2_2 - Chapter 2 Fundamentals of Logic The rules of...

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Chapter 2. Fundamentals of Logic. The rules of logic give precise meaning to mathematical statements. We need to study logic to learn how to construct valid reasoning. Logic focuses on the relationship between propositions (not the content of any particular proposition) Logical methods are used in mathematics to prove theorems and in computer science to prove that programs do what they supposed to do Definition . A proposition ( or a statement ) is a sentence that is either true or false, but not both. (Boolean variables)

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Which of the following are propositions? Two is a prime number. How are you? x +1=2. There is life on Saturn n 2 + n +41 is a prime number for all natural numbers, 2200 n N (like any statement, this one relies upon some definitions, terminology and notations)
Let p , q , r , … be propositions. Compound statements can be formed using binary connectives (operators): (and) (inclusive or) (implication) (biconditional) and unary operator ¬ (negation) Logic is the algebra of propositions ( Boolean algebra )

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