Lesson 5.1 Introduction to Reasoning pp. 160-166

1. Lesson 5.1 Introduction to Reasoning pp. 160-166

2. Objectives: 1. To define reasoning (logical thinking). 2. To apply tables, diagrams, and educated guesses as tools in reasoning through logic problems.

3. Definition Reasoning is the step-by-step process that begins with a well known fact or assumption and builds to a conclusion in an orderly, concise way. This is also called logical thinking.

4. Memorial Hospital employs 37 doctors and 59 women. Of 15 employees under 25 years of age, 9 are not doctors. Dr. Novak is the only woman doctor under the age of 25, though 10 other doctors are women. How many doctors are over 25?

5. 1. Identify the three main sets. Doctors  37 Women  59 under 25  15

6. Y = 15 W = 59 D = 37 2. Draw a Venn diagram and complete as much of the diagram as possible.

7. 2. Draw a Venn diagram and complete as much of the diagram as possible. Y = 9 W = 59 6 D = 31

8. Y = 9 W = 58 D = 31 2. Draw a Venn diagram and complete as much of the diagram as possible. 1 5

9. Y = 9 W = 48 D = 21 2. Draw a Venn diagram and complete as much of the diagram as possible. 1 5 10

10. 3. How many doctors are over the age of 25? 31 Y = 9 W = 48 1 5 10 D = 21

11. Example: Bob, Jim, Phil, and Brent are part of the crew of a commercial tugboat. Their jobs, not in any particular order, are captain, first mate, cook, and mechanic. The mechanic is the first mate’s younger brother. The captain has no relatives on the crew, but Brent does. The first mate is not the cook’s uncle, and the cook is not the mechanic’s uncle, but Bob is Phil’s uncle. What job does each man have, and how are the men related to each other?

12. First Mate (bro. to mechanic- not cook’s uncle) Mechanic (bro. to first mate-not cook’s nephew) Cap. Cook Bob (Phil’s uncle) Jim Phil (Bob’s nephew) Brent                

13. Homework pp. 163-166

14. Lance, Terri, Jen, and Kelly prefer each a different type of nut. Lance detests almonds, Kelly likes cashews, Jen cares neither for almonds nor walnuts. 1. Who likes pecans? 2. What does Lance like?

15. Questions 1 & 2 almonds cashews walnuts pecans     Lance Terri Jen Kelly             Jen likes pecans and Lance likes walnuts.

16. G K A U #10 50 mothers 5 12 8 7 6 1 11

17. ■ Cumulative Review A = {4, 5, 6, 7, 8} B = {3, 5, 7, 9} C = {1, 2} U = {1, 2, 3,...,9} Find the following. 15. A′

18. ■ Cumulative Review A = {4, 5, 6, 7, 8} B = {3, 5, 7, 9} C = {1, 2} U = {1, 2, 3,...,9} Find the following. 16. A  B

19. ■ Cumulative Review A = {4, 5, 6, 7, 8} B = {3, 5, 7, 9} C = {1, 2} U = {1, 2, 3,...,9} Find the following. 17. C  B

20. ■ Cumulative Review A = {4, 5, 6, 7, 8} B = {3, 5, 7, 9} C = {1, 2} U = {1, 2, 3,...,9} True/False. 18. A  B = C′

21. ■ Cumulative Review A = {4, 5, 6, 7, 8} B = {3, 5, 7, 9} C = {1, 2} U = {1, 2, 3,...,9} Find the following. 19. 7  A

22. ■ Cumulative Review A = {4, 5, 6, 7, 8} B = {3, 5, 7, 9} C = {1, 2} U = {1, 2, 3,...,9} Find the following. 20. 2  C

23. ■ Cumulative Review A = {4, 5, 6, 7, 8} B = {3, 5, 7, 9} C = {1, 2} U = {1, 2, 3,...,9} Find the following. 21. {3, 4}  A  B