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Name _______________________________ Hour ______ 2-4 Worksheet Determine whether each conclusion is based on inductive or deductive reasoning. 1. Aundrea noticed that every Saturday, her neighbor mows his lawn. Today is Saturday. Aundrea concludes her neighbor will mow his lawn. 2. Students at Blake’s high school must have a B average in order to participate in sports. Blake has a B average, so he concludes that he can participate in sports at school. 3. At Uriah’s school if you are late five times, you will receive a detention. Uriah has been late to school five times; therefore he will receive a detention. 4. A dental assistant notices a patient has never been on time for an appointment. She concludes that the patient will be late for her next appointment. 5. If Cooper decides to go to a concert tonight, he will miss football practice. Tonight, Cooper went to a concert. Cooper missed football. 6. Whenever Nicole has attended a tutoring session she notices that her grades have improved. Nicole attends a tutoring session and she concludes her grades will improve. 7. Every Wednesday Kelsy’s mother calls. Today is Wednesday, so Kelsy concludes her mother will call. Use the Law of Detachment to draw a conclusion. 8. If a student gets an A on a final exam, then the student will pass the course. Samuel get an A on the music theory final exam. What can you conclude? 9. If a student wants to go to college, then the student must study hard. Josiah wants to go to Oklahoma State University. What can you conclude? 10. If two lines are parallel, then they do not intersect. Line a is parallel to line b. What can you conclude? 11. If there is lightening, then it is not safe to be out in the open. Luke sees lightening from the soccer field. What can you conclude? Determine whether the stated conclusion is valid or invalid based on the given information. 12. Given: If a number is divisible by 6, then the number is divisible by 3. 18 is divisible by 6. Conclusion: 18 is divisible by 3. 1 13. Given: If a pet is a rabbit, then it eats carrots. Jessica’s pet eats carrots. Conclusion: Jessica’s pet is a rabbit. 14. Given: if a dog eats Superdog Dog Food, then he will be happy. Jake is a happy dog. Conclusion: Jake eats Superdog Dog Food. 15. Given: if you leave your lights on while your car is off, then your battery will be dead. Your battery is dead. Conclusion: You left your lights on while the car was off. 16. Given: If 75% of the prom tickets are sold, the prom will be held at the country club. 75% of the prom tickets were sold. Conclusion: The prom will be held at the country club. Use the Law of Syllogism to draw a conclusion. 17. If an animal is a red wolf, then its scientific name is Canis Rufus. If an animal is named Canis Rufus, then it is endangered. 18. If you read a good book, then you enjoy yourself. If you enjoy yourself, then your time is well spent. 19. If two angles form a linear pair, then the two angles are supplementary. If two angles are supplementary, then the sum of their measures is 180. 20. If a hurricane is Category 5, then winds are greater than 155 miles per hour. If winds are greater than 155 miles per hour, then trees, shrubs, and signs are blown down. Use the Law of Syllogism to draw a valid conclusion. If no valid conclusion can be drawn write no valid conclusion. 21. If you interview for a job, then you wear a suit. If you interview for a job, then you will update your resume. 22. If Tram has a grade point average of 3.0 or greater, then she will be on the honor roll. If Tram is on the honor roll, then she will have her name in the school paper. 23. If the measure of an angle is between 90 and 180, then it is obtuse. If an angle is obtuse, then it is not acute. 2 24. If a number ends in 0, then it is divisible by 2. If a number ends in 4, then it is divisible by 2. Using Logical Reasoning. Use the Venn diagram to answer the following questions. Work After School 5 3 Work Weekends 17 The Venn diagram shows the number of students in the band who work after school or on weekends. 24. How many students work after school and on the weekends? 25. How many students work after school or on the weekends? For exercises 26 - 31, assume that the following statements are true. A. B. C. D. E. If Maria drinks juice, then it is breakfast time. If it is lunchtime, then Kira drinks milk and nothing else. If it is mealtime, then Curtis drinks water and nothing else. If it is breakfast time, then Julio drinks juice and nothing else. Maria drinks juice. Use only the information given above. For each statement write must be true, may be true, or not true. 26. Julio drinks juice. 27. Curtis drinks water. 28. Kira drinks milk. 29. Curtis drinks juice. 30. Maria drinks water. 31. Julio drinks milk. 3