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Write the following in biconditional form.

Write the following in biconditional form. p: The sun is out. q: It is day time. The sun is out iff it is day time. Deductive Reasoning. Geometry Unit 9, Day 9 Mr. Zampetti. Objectives. Learn and Use Law of Detachment Learn and Use Law of Syllogism. Definition.

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Write the following in biconditional form.

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  1. Write the following in biconditional form. • p: The sun is out.q: It is day time. • The sun is out iff it is day time.

  2. Deductive Reasoning Geometry Unit 9, Day 9 Mr. Zampetti

  3. Objectives • Learn and Use Law of Detachment • Learn and Use Law of Syllogism

  4. Definition • Deductive Reasoning – to reach a logical conclusion by using facts, rules, definitions, or properties. • Remember: Inductive Reasoning uses examples to make conjectures!

  5. Laws • Law of Detachment and Law of Syllogism are both a form of deductive reasoning that is used to draw conclusions from true conditional statements.

  6. Law of Detachment • If pq is true AND p is true, then q is also true. • In symbols: [(pq)^p]  q

  7. Determine if the Conclusion is Valid • We know: If a ray is an angle bisector, then it divides the angle into two congruent angles. • Given: BD bisects ABC Conclusion: ABD  CBD Valid?

  8. Cont. • Given: PQT  RQS Conclusion: QS and QT are angle bisectors. Valid?

  9. Law a Syllogism • If pq and qr are true, then pr is also true • In symbols: [(pq)^(qr)]  (pr) • This is similar to the Transitive Property

  10. Use Law of Syllogism to determine whether a valid conclusion can be reached: • Given: (1) If the symbol of a substance is PB, then it is lead. (2) The atomic number of lead is 82. • Hint: use letters to represent the parts of a statement:p: the symbol of a substance is PBq: it is leadr: the atomic number is 82. • Can there be a valid conclusion?

  11. Use Law of Syllogism to determine whether a valid conclusion can be reached: • Given: (1) Water can be represented as H2O. (2) Hydrogen, H, and oxygen, O, are in the atmosphere. • Can there be a valid conclusion?

  12. Example • 1. If you drive safely, then you can avoid accidents.2. Tim drives safely.3. Tim can avoid accidents. • Law of Detachment!

  13. Example • 1. If you are a customer, then you are always right2. If you are a teenager, then you are always right3. If you are a teenager, then you are a customer • INVALID

  14. Example • 1. If you are an athlete, then you work out.2. If you work out, then you are in shape.3. If you are an athlete, then you are in shape. • Law of Syllogisms

  15. Homework • Work Packet: Deductive Reasoning

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