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.

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Presentation transcript:

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

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.

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

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?

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

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

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 PB q: it is lead r: the atomic number is 82. Can there be a valid conclusion?

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?

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

Example 1. If you are a customer, then you are always right 2. If you are a teenager, then you are always right 3. If you are a teenager, then you are a customer INVALID

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

Homework Work Packet: Deductive Reasoning