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(1.4) An Introduction to Logic

(1.4) An Introduction to Logic. Logic is a tool that allows us to apply mathematical reasoning in problem solving. Definition : A statement is a sentence that is either true or false, but not both. Example (i) : Which of the following are statements?

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(1.4) An Introduction to Logic

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  1. (1.4) An Introduction to Logic Logic is a tool that allows us to apply mathematical reasoning in problem solving. Definition: A statement is a sentence that is either true or false, but not both. Example (i): Which of the following are statements? Definition: If p is a statement then ~p is the negation of p. Negation means making the opposite statement.

  2. Example (ii): Negate each of the following statements. • Definition: There are two types of quantifiers that appear in sentences. • Universal quantifiers: all, every, no, none • Existential quantifiers: some, there exists StatementNegation

  3. Definition: There are two ways to create compound statements by using connections. • Conjunction: p Λ q means statement p AND statement q. • Disjunction: p V q means statement p OR statement q.

  4. Contrapositive (p --> q) is equivalent to (~q --> ~p) ____________________________________________ Statement: If p then q. (p --> q) Converse: If q then p. (q --> p) Inverse: If not p then not q. (~p --> ~q) Contrapositive: If not q then not p. (~q --> ~p)

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