If your cable company keeps you on hold, then you get _________. If you get _________, then you go _______________. If you go _______________, then accidents __________. If accidents ___________, then you get an ___________. If you get an ____________, then people think you’re _________. If people think you’re _________, people want to see _____________. If people want to see _____________, then you wake up in a ____________________. What do you think the conclusion is?: If ____________________________________, then _________________________________. angry blow off steam happen eye patch tough how tough roadside ditch

Section 2-4: 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 two angles are adjacent, then they share a common vertex. and share a common vertex. 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 _________________________ 1.) 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. (p - hypothesis, q - conclusion)

2.) 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. 3.) If two angles are supplementary, then their sum is 180. If two angles are a supplementary, then they are adjacent. Conclusion: __________________________________ p q p r Not possible p  q, but q  r

If possible, use the Law of Syllogism to draw a conclusion. If not possible, write not possible. 4.) 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

Using the Laws of Syllogism and Detachment a river is more than 4000 mi long it is longer than the Amazon it is the longest river in the world mi long is the longest river in the world.

5.) What can you conclude from the given information? If a student is on the basketball team, then he has practice after school. If there is practice after school, then the student needs to take the late bus. Luke is on the basketball team. Luke needs to take the late bus.Conclusion: ____________________________________

If your cable company keeps you on hold, then you get angry. If you get angry, then you go blow off steam. If you go blow off steam, then accidents happen. If accidents happen, then you get an eye patch. If you get an eye patch, then people think you’re tough. If people think you’re tough, people want to see how tough. If people want to see how tough, then you wake up in a roadside ditch. Back to the intro… If you were to apply the Law of Syllogism throughout the entire series of statements above, adding more letters than p, q, and r’s, what would your final conclusion be? Do you agree with your answer on Slide 1? ______________________________________________________________________ If your cable company keeps you on hold, then you wake up in a roadside ditch.