Section 2-3: 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 If a conditional statement is _______ and the hypothesis is _______, then its conclusion is ________. true Law of Detachment If p  q is a true statement, and p is true, then q is true

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. pq A Jeep is a car. p q 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. pq p q

If possible, use the Law of Detachment to draw a conclusion. If not possible, write not possible. 3.) If Spot is a dog, then he has four legs. Spot has four legs. Conclusion: _____________________________Not possible pq q 4.) If a student takes Geometry, then he feels fulfilled. John feels fulfilled. Conclusion: _____________________________ Not possible pq q

Law of Syllogism____________________ If p  q and q  r are true statements, then p  r is a true statement Transitive Propertysimilar to the _________________________ 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, then p  r it is a rectangle.

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, thenp  r they live in the United States. p q q r If possible, use the Law of Syllogism to draw a conclusion. If not possible, write not possible. 7.) If two angles are a linear pair, then their sum is 180. If two angles are a linear pair, then they are adjacent. Conclusion: __________________________________ p q p r Not possiblep  q, but q  r

If possible, use the Law of Syllogism to draw a conclusion. If not possible, write not possible. 8.) If you are studying Algebra, then you are studying mathematics. If you are studying Geometry, then you are studying mathematics. Conclusion: _____________________________ Not possible pq qr p  q, but r  q

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.) __________________________________________________________ ____________________________________________________________