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Chapter 3: Logic

Chapter 3: Logic. 3.1 Statements and Quantifiers 3.2 Truth Tables. Statement. A statement is a declarative sentence that is either true or false. Examples: Mr. Healey is my math teacher. It is sunny today in Narragansett. 2 + 8 = 10 The Patriots lost this past weekend.

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Chapter 3: Logic

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  1. Chapter 3: Logic 3.1 Statements and Quantifiers 3.2 Truth Tables

  2. Statement • A statement is a declarative sentence that is either true or false. • Examples: • Mr. Healey is my math teacher. • It is sunny today in Narragansett. • 2 + 8 = 10 • The Patriots lost this past weekend.

  3. Examples of sentences that aren’t statements: Paint the wall. Paul Pierce is better than Ray Allen.

  4. Compound Statements • May be formed by combining two or more statements using logical connectives. • And , or, not, if…then are examples of connectives.

  5. Negations The negation of a true statement is false. The negation of a false statement is true.

  6. Examples of Negations “Tom Jones has a red car.” The negation would be: “Tom Jones does not have a red car” “The sun is a star” The negation would be: “The sun is not a star.”

  7. Negations with inequalities

  8. Symbols

  9. Using symbols to make logic statements • Let p represent “It is 80 degrees today” and let q represent “It is Tuesday.” • Write each symbolic statement in words. • p V q • ~p Λ q • ~(p V q) • ~(p Λ q)

  10. Negation of Quantified Statements

  11. 3.2 Truth Tables Truth tables give every outcome for specific compound statements. Today we will look at AND, OR, and the NEGATION truth tables.

  12. When is an “and” statement true? Example: I went to Florida and saw a Red Sox game.

  13. When is an “OR” statement true? I own a Nissan or I own a Ford.

  14. Negation Truth Table

  15. Assignment! P103-105 1-14, 23-35odd, 43,4447,49,52, 57, 58, 59, 67-72. P115-116: 7-15

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