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Section 2-5: Deductive Reasoning Goal: Be able to use the Law of Detachment and the Law of Syllogism. Inductive Reasoning uses _________ to make conclusions. Deductive Reasoning uses ___________ to make conclusions. rules ____________________ examples hypothesis conclusion true Law of Detachment If the ____________ of a true if-then statement is _______, then the ___________ is also ______. true
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Use the Law of Detachment to draw a conclusion. 1.) If a vehicle is a car, then it has four wheels. Conclusion: _____________________________A Jeep has four wheels. true A Jeep is a car. true 2.) If two lines are parallel, then they do not intersect. Line m is parallel to line n. Conclusion: _____________________________Line m and line n do not intersect. true
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3.) Which argument is correct? Explain your reasoning. Argument 1: If two angles form a linear pair, then they are supplementary. and form a linear pair. So, and are supplementary. Argument 2: If two angles form a linear pair, then they are supplementary. and are supplementary. So, and form a linear pair. In Argument 1, the hypothesis is true, which implies the conclusion is true. Argument 2 is false because two nonadjacent angles could be supplementary, for example 30° and 150°, but not form a linear pair.
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4.) Which argument is correct? Explain your reasoning. Argument 1: If two angles measure 70° and 110°, then the angles are supplementary. and are supplementary. So and Argument 2: If two angles measure 70° and 110°, then the angles are supplementary. The and. So, and are supplementary. In Argument 2, the hypothesis is true, which implies the conclusion is true. Argument 1 is false because angle 1 could be 60° and angle 2 120°. They are supplementary, but their measures are not 70° and 110°.
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Law of Syllogism_______________ 5.) If a quadrilateral is a square, then it contains four right angles. Use the Law of Syllogism to draw a conclusion. If a quadrilateral contains four right angles, then it is a rectangle. Conclusion: __________________________________ _____________________________________________ pq qr If a quadrilateral is a square,If p, then r. then it is a rectangle. If statement p, then statement q. If statement q, then statement r. If statement p, then statement r. If these statements are true, then this statement is true
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6.) If people live in Vernon Hills, then they live in Illinois. If people live in Illinois, then they live in the United States. Conclusion: __________________________________ _____________________________________________ If people live in Vernon Hills,If p, then r. then they live in the United States. p q r q As a group, write your own conclusions based on the Law of Detachment and the Law of Syllogism. Each group member will take a turn in creating a sentence that makes sense in reaching a conclusion.
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Write your own example to illustrate the correct use of the Law of Detachment. Write your own example to illustrate the correct use of the Law of Syllogism. 1.) __________________________________________________________ ____________________________________________________________ 2.) __________________________________________________________ 3.) __________________________________________________________ ____________________________________________________________ 1.) __________________________________________________________ ____________________________________________________________ 2.) __________________________________________________________ ____________________________________________________________ 3.) __________________________________________________________ ____________________________________________________________
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