Review for Final

You are not required to hand this review in. But, you may if you would like to check yourself and build your confidence. You will not recieve extra credit. (Or any credit of any sort) (200 pretend points total)

If you do not complete the review, at least look at the final exam tips at the end.

Chapter 1:

A. Determine whether the following arguments are inductive or deductive. Abstract form from the content and identify the premises and the conclusion (P¹, P², . . . C) and determine whether valid/invalid or strong/weak: (Three points each)

1. This clay tile looks exactly like the tile I laid on my patio last summer, and it's made by the same manufacturer. Since the tile on my patio scratches very easily, it is likely that this tile will also scratch easily. I don't advise that you buy it.

2. Highway 14 cannot be the road to Springtown. The road to Springtown is a gravel road and Highway 14 is paved.

3. Since Greenville is one mile from Central City, and Central City is one mile from Harristown, it follows necessarily that Greenville is two miles from Harristown.

4. The National Questioner (known for its sensationalist journalism) reports that a young boy in Oklahoma has spoken with martians. Thus, we must draw the conclusion that martians do indeed exist.

5. Since some politicians are honest people and some honest people are eloquent statesmen, it follows that some politicians are eloquent statesmen.

6. Last night the water pipes in the basement burst. Since the temperature outside was well below zero at that time, the conclusion is warranted that the damage was caused by freezing.

7. Most of the students attending Shoreline Prep have extremely wealthy parents. Since Madeline is a student at Shoreline, it is likely that her parents are wealthy.

8. Since figure A is a square and the length of one of its sides is exactly one inch, it follows that its area is exactly one square inch.

9. According to a two hundred year old tradition, the president of the Apex Club has always been a woman. Therefore, the next president will most likely be a woman.

10. Laura sneezed a few minutes ago, and now she's blowing her nose. Laura must have pneumonia.

B. Use the counter-example method to prove that the following argument is invalid. . (10 points)

 

Some soft drinks are not beverages that contain caffeine, and some beverages that contain caffeine are not drinks flavored with grapefruit juice. Therefore, some soft drinks are not drinks flavored with grapefruit juice.

Chapter 3:

C. From the following list, identify which fallacies occur in the following arguments: (One point each)

1. Immediate steps should be taken to reduce this country's dependence on nuclear power. The question was put to six prominent movie stars recently, and all six agreed that nuclear power was extremely dangerous.

2. How long have you been plagiarizing your term papers?

3. That carpet in the store window was manufactured by the same company as the carpet I presently have on my floors. The carpet on my floors has lasted for ten years. Therefore, if I install the carpet which is in the store window, it will probably last for ten years.

4. Advertisements claim that the new Pride detergent gets your clothes whiter and brighter than any other brand. Since no one has disproved this claim, we must conclude that it is true.

5. Both wolves and hyenas are cunning and dangerous. Therefore, wolves are cunning.

6. Paul told me that he loves his children more than his wife. It must be the case that his wife doesn't like the kids.

7. Strenuous exercise is good for people. Therefore, it would be a good idea for old Mrs. Bevans, who just had a heart attack, to go jogging today.

8. The decision as to what courses should be required of all university students should be left to the faculty senate. If students are given a voice in this matter it won't be long before the students dictate who should be hired and fired. In no time they'll take over the administrative functions as well, and the university will collapse.

9. Senator Collins supports the proposal for the new B-2 bomber. But his arguments in favor of this project should be discounted, since the primary bidder on the B-2 bomber comes from the state he represents.

10. Every ingredient in this pastry is fattening. Therefore, this pastry is fattening.

11. As a spokesman for the IRS, I would urge that you stop informing taxpayers of these loopholes we have been discussing. I am confident you will comply, since surely you want to avoid an audit of your last year's return.

12. Surely God does not exist. Just look at all the suffering in the world.

13. Either the United States continues to send billions of dollars in military aid to Central American countries or these countries will all turn Communist and be our mortal enemies. Surely you don't want that to happen. Therefore, you agree that the United States must continue sending billions of dollars in military aid to Central American countries.

14. A recent study has shown that among the youth of our city, 80 percent of those who contracted venereal disease last year had taken sex education classes in high school. Obviously if we want to cut down on the incidence of V.D. we must get rid of those sex education classes.

15. Milton Friedman is famous for his argument that corporations should not have to pay income taxes. But this argument is not worth a plugged nickel. Corporations in America are gettting away with murder as it is. Consider the utilities. Those companies are supposed to be regulated by state commissioners, but the commissioners never do their job. They give the utilities whatever they want. If the members of the Public Utilities Commission were elected by the people we wouldn't have such astronomical rates.

16. It would not be a good idea to appoint Frances McGill to the office of city manager. During the past fifteen years McGill has managed five different businesses, and all of them declared bankruptcy as a direct result of her inept leadership.

17. The Balboa Suspension Bridge was constructed using the strongest steel available. Thus, the bridge must be extremely strong.

18. Actresses are persons and Jennifer is a great actress. Thus, she must be a great person.

19. Either this key fits the front door or it's the wrong key. But it clearly doesn't fit. It's much too large. Therefore, it's the wrong key.

20. Mr. Referee, surely you won't call our team offside on that last play. Our team has already had ten penalties this quarter, and we're trailing by three touchdowns.

Chapter 4: (Five points each)

D. For the following statements:

a. Identify the type of statement (A, E, I or O).

b. Identify the quantity and quality.

c. Change the quality but not the quantity.

d. Change the quantity but not the quality.

e. Change both the quality and the quantity.

1. All joggers are athletes.

2. Some motion pictures are comedies.

3. No cabbages are pine trees.

4. Some true statements are not believable statements.

E. Draw the traditional square of opposition labeling as much as you can. (Try to do this from memory--will be necessary for final. (10 points total)

 

 

 

 

F. Using the square and conversion, obversion and contraposition determine whether the following arguments are valid or invalid: name the fallacy committed. Then check your work with Venn diagrams. (8 points total)

1. All commodity traders are gamblers who risk sudden disaster. Therefore, all gamblers who risk sudden disaster are commodity traders.

2. No child abusers are persons who belong in day-care centers. Therefore all child abusers are persons who do not belong in childcare centers.

3. It is false that some orthodox psychoanalysts are not individuals driven by religious fervour. Therefore it is false that allorthodox psychoanalysts are individuals driven by religious fervor.

4. It is false that some wood ticks are not carriers of lymes disease. So, some wood ticks are carriers of lymes disease.

 

Chapter 5:

G. Put the following categorical syllogisms into standard form and identify the mood and figure of each. (One point each)

1. The reason that some cats are not black animals is because all dogs are black animals and some cats are not dogs.

2. All dogs are animals that have tails, so all cats are animals that have tails because all cats are dogs.

3. No animals are purple creatures and all cats are animals, so no cats are purple creatures.

4. Some cats are white animals because some dogs are white animals and some cats are dogs.

5. Some cats are not black animals and some dogs are not cats. It follows then that no dogs are black animals.

 

H. Use Venn diagrams to determine whether the following arguments are valid or invalid. (Two points each)

1. All M are P.

Some S are M.

Some S are not P.

2. No P are M.

All S are M.

Some S are not P.

3. Some P are M.

All S are M.

Some S are P.

4. No M are P.

All M are S.

Some S are not P.

5. Some P are M.

No M are S.

Some S are P.

I. Memorize the five rules. Reconstruct the following syllogisms and use the rules to determine whether they are valid or invalid. (Three points each)

1. AAA-1

2. EAE-2

3. IEA-4

4. AOI-3

5. IEO-4

Chapter 6:

J. Translate the following statements into symbolic form: (One point each)

1. Argentina will reduce unemployment and Brazil will cut taxes, or Columbia will support agrarian reform.

2. Argentina will reduce unemployment if either Brazil cuts taxes, or Columbia supports agrarian reform.

3. Argentina will reduce unemployment and Brazil will cut taxes provided that Columbia supports agrarian reform.

4. If Argentina reduces unemployment then if Brazil cuts taxes then both Columbia will support agrarian reform and the Dominican Republic will increase government spending.

5. If Argentina's reducing unemployment implies that either Brazil cuts taxes or Columbia supports agrarian reform, then the Dominican Republic will increase government spending.

K. Determine the truth values of the following symbolized statements. A and B are true while X and Y are false. (Two points each)

1. [(A É X) v (Y É B)] º ~[(A v X) · (B v Y)]

2. [(A · X) v (B · ~Y)] É [(A º ~X) · (Y º ~B)]

3. ~[(A v ~B) · (X v ~Y)] º [(X É ~Y) · (A É ~B)]

4. ~{[(A · X) v (B É ~Y)] · [(Y º ~B) É (X v A)]}

5. ~[(Z É A) · (B É ~Y)] º ~[~(B · Z) É (~Y · ~A)]

L. Use extended, regular truth tables to determine whether the following arguments are valid or invalid. (Three points each)

1. A º ~B / A v B // B · ~A

2. A É B / B É C / A v C // B v C

3. A v B / B É ~A // A º ~B

4. A É B / B É ~C / ~B ·  C // A v B

5. A É (B · ~C) / B É C // ~A

 

M. Use indirect truth tables to determine whether the following arguments are valid or invalid. (Two points each)

1. (A v B) · (D v E) / C É ~ E / A É (F · ~D) / ~C v ~A // A É B

2. E É (C v D) / C É (B v D) / D É B / ~B v (E · C) // C º  E

3. (A · B) v (C ·  D) / B É (E ·  F) / D É (G · H) // F v H

4. A v B / A É  (C ·  D) / B É (E · F) // D ·  F

5. (A v B) É (C v D) / C É (D · E) / (E v F) É G // A É G

Chapter 7:

N. Using the 18 rules of inference, derive the conclusions of the following symbolized arguments: (Three points each)

(1) 1. D v ~C

2. (A · B) É C

3. A /B É D

(2) 1. A v (B ·  C)

2. (~A É B) É (C v ~D)

3. D /C v X

(3) 1. A º B

2. A v B

3. A É (B É C) /C

(4) 1. (A ·  B) É C

2. B · ~C

3. (~C · ~D) É A /D

(5) 1. ~(~A ·  B)

2. ~(~C · ~B)

3. (A É D) · (C É E) /D v E HINT: Use DM and Implication

O. Translate the following argument into symbolic form and prove that it is valid using natural deduction. (15 points)

Either the ancient etruscans were experienced city planners and they invented the art of writing or they were highly skilled engeneers and they invented the art of writing. If the ancient Etruscans were bloodthirsty numskulls (as scholars once thought), they did not invent the art of writing. Therefore, the ancient etruscans were not bloodthirsty numskulls.

Phew! CONGRATULATIONS!! IF you have worked down to here (and did the exercises correctly ) you are certainly ready for the final!

FINAL EXAM TIPS

ü There will be a list of informal fallacies with the exam.

ü There will be a list of Rules of Inference for working proofs.

ü Among the things you wil need to memorize are:

Four types of Categorical Propositions including:

Type

Quantity

Quality

Distribution

Four Figures of Standard Form Categorical Syllogisms

· Rules for Categorical Syllogisms

Traditional Square of Opposition

Conversion, obversion and contraposition

How to set up truth tables

Truth-functional definitions of the five connectives

The problems on the final exam will be similar to those in the preceding review. No other types of problems will be on the exam.

Good luck!

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