Lesson 5.1Introduction to Reasoning

pp. 160-166

Lesson 5.1Introduction to Reasoning

pp. 160-166

Objectives:1. To define reasoning (logical

thinking).2. To apply tables, diagrams, and

educated guesses as tools in reasoning through logic problems.

Objectives:1. To define reasoning (logical

thinking).2. To apply tables, diagrams, and

educated guesses as tools in reasoning through logic problems.

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.

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.

DefinitionDefinitionDefinitionDefinition

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?

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?

1. Identify the three main sets.1. Identify the three main sets.

Doctors 37

Women 59

under 25 15

Doctors 37

Women 59

under 25 15

2. Draw a Venn diagram and complete as much of the diagram as possible.

2. Draw a Venn diagram and complete as much of the diagram as possible.

Y = 15Y = 15 W = 59W = 59

D = 37D = 37

2. Draw a Venn diagram and complete as much of the diagram as possible.

2. Draw a Venn diagram and complete as much of the diagram as possible.

Y = 9Y = 9 W = 59W = 59

D = 31D = 31

66

2. Draw a Venn diagram and complete as much of the diagram as possible.

2. Draw a Venn diagram and complete as much of the diagram as possible.

Y = 9Y = 9 W = 58W = 58

D = 31D = 31

55 11

2. Draw a Venn diagram and complete as much of the diagram as possible.

2. Draw a Venn diagram and complete as much of the diagram as possible.

Y = 9Y = 9 W = 48W = 48

D = 21D = 21

551010

11

3. How many doctors are over the age of 25?

3. How many doctors are over the age of 25?

Y = 9Y = 9 W = 48W = 48

D = 21D = 21

551010

11

3131

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?

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?

First Mate(bro. to mechanic-not cook’s uncle)

First Mate(bro. to mechanic-not cook’s uncle)

Mechanic(bro. to first mate-not cook’s nephew)

Mechanic(bro. to first mate-not cook’s nephew)Ca

p.Ca

p.

Cook

Cook

Bob(Phil’s uncle)

Bob(Phil’s uncle)

JimJim

Phil(Bob’s nephew)

Phil(Bob’s nephew)

BrentBrent

Homeworkpp. 163-166Homeworkpp. 163-166

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?

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?

LanceTerriJen

Kelly

LanceTerriJen

Kelly

almonds cashews walnuts pecansalmonds cashews walnuts pecans

Questions 1 & 2Questions 1 & 2

Jen likes pecans and Lance likes walnuts.Jen likes pecans and Lance likes walnuts.

#10#10

UU

GG KK

AA

50 mothers50 mothers

1212

1111

8877

55

66 11

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} Find the following.

15. A′

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} Find the following.

15. A′

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} Find the following.

16. A B

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} Find the following.

16. A B

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} Find the following.

17. C B

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} Find the following.

17. C B

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} True/False.

18. A B = C′

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} True/False.

18. A B = C′

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} Find the following.

19. 7 A

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} Find the following.

19. 7 A

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} Find the following.

20. 2 C

■ Cumulative ReviewA = {4, 5, 6, 7, 8} B = {3, 5, 7, 9}C = {1, 2} U = {1, 2, 3,...,9} Find the following.

20. 2 C

■ Cumulative ReviewA = {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

■ Cumulative ReviewA = {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