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Geometry Chapter 2

Geometry Chapter 2. Logic and Reasoning. Vocabulary. Example 1: Identifying the Parts of a Conditional Statement. Identify the hypothesis and conclusion of each conditional. A. If today is Thanksgiving Day, then today is Thursday. Hypothesis: Today is Thanksgiving Day.

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Geometry Chapter 2

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  1. Geometry Chapter 2 Logic and Reasoning

  2. Vocabulary

  3. Example 1: Identifying the Parts of a Conditional Statement Identify the hypothesis and conclusion of each conditional. A. If today is Thanksgiving Day, then today is Thursday. Hypothesis: Today is Thanksgiving Day. Conclusion: Today is Thursday. B. If a number is an integer, then it is a rational number. Hypothesis: A number is an integer. Conclusion: The number is a rational number.

  4. More Vocabulary

  5. More Vocabulary

  6. Conditional p q • If I studied, then I did well in Geometry. • Converse q p • If I did well in Geometry, then I studied. • Inverse ~p ~q • If I did not study, then I did not do well in Geometry. • Contrapositive ~q ~p • If I did not do well in Geometry, then I did not study. Example

  7. Write 8 sets of conditional statements like the last example. Each set should have 4 sentences: conditional, converse, inverse, and contrapositive. Be sure to label each sentence with what type of logical statement it is. • This must be finished and turned in by the end of class today. Classwork for Logic

  8. Not all logic statements are true. Oftentimes, if the conditional statement is true, then the converse is not true. • Example) • Conditional: If you are a human, then you have hair. • Converse: If you have hair, then you are human. Truth of Logic Statements

  9. A counterexample shows that the conclusion of a logic statement is false. • If you have hair, then you are human. • Counterexample: bears have hair Truth of Logic Statements

  10. If a conditional statement and its converse are both true, we call that statement a bi-conditional statement. • Conditional: If there is thunder, then there is lightning. • Converse: If there is lightning, then there is thunder. • Bi-conditional: There is thunder if and only if there is lightning. Truth of Logic Statements

  11. pq means p q and qp A bi-conditional statement is written in the form “p if and only if q.” This means “if p, then q” and “if q, then p.” Symbols Converse Conditional Bi-conditional Truth of Logic Statements

  12. Conditional: If a figure has three sides, then it is a triangle. • Converse: If a figure is a triangle, then it has three sides. • Bi-conditional: Truth of Logic Statements

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