Test 4 Review Sets and Logic

a. 8 b. 7

Given a set A = { n ,6, I }, answer the following questions: a. Find the number of subsets of A = _________ b. Find the number of proper subsets of A = ______

Therefore, no sailors are miserly.

Supply a conclusion to make each argument valid: All sailors are big spenders. No big spenders are miserly.

Therefore, Tiger is appetizing.

Supply a conclusion to make each argument valid: All shrimp are appetizing. Tiger is a shrimp.

Therefore, some flowers are blue.

Supply a conclusion to make each argument valid: All violets are blue. Some flowers are violets.

Therefore, no New Yorkers are Southerners

Supply a conclusion to make each argument valid: No New Yorker likes pecan pie. All Southerners like pecan pie.

post hoc

The oven was working fine until you started using it, so you must have broken it.

10

n(A∩B')=

post hoc

During the Gulf war many Americans made immense profits. That is an indisputable fact. Therefore, there can be no doubt that American business interests instigated the war.

2^k-1

How do you find the number of proper subsets in a set?

2^k

How do you find the number of subsets in a set?

false dilemma

I can see that you are in the market for a new car. We're having a sale on Pintos this month. Do you want to pay cash or do you want the installment plan?

Inverse

If not p, then not q. Ex: If you aren't in this class, then you don't go to JT.

Contrapostive

If not q, then not p

Statement

If p then q Ex: If you are in the class, then you attend John Tyler.

Converse

If q then p Ex: If you attend JT, then you are in this class

circular reasoning

What is right is what is morally obligatory. What is morally obligatory is what you should do. Of course, you should do something because it is the right thing to do.

Valid

Determine if the conclusion follows logically from the premises. Premise: If it is raining, then the grass will be wet Premise: The grass is dry Conclusion: It is not raining

Invalid argument

Determine if the conclusion follows logically from the premises. Premise: No loving persons are thoughtless persons. Premise: No loving persons are aggressive people. Conclusion: No aggressive people are thoughtless persons.

Valid argument

Determine if the conclusion follows logically from the premises: All children are energetic. Some actors are children. Therefore, some actors are energetic.

Invalid argument

Determine if the conclusion follows logically from the premises: All flowers need water. Roses need water. Therefore, roses are flowers.

Invalid argument

Determine if the conclusion follows logically from the premises: Jim is getting married or Sally is finding a new boyfriend. Sally is finding a new boyfriend. Therefore, Jim is not getting married.

Valid argument

Determine if the conclusion follows logically from the premises: Kelly is a poet or Kathy is a cheerleader. Kathy is not a cheerleader. Therefore, Kelly is a poet.

Invalid

Determine whether each argument is valid or invalid: All Hawaiians eat SPAM. Some Californians eat SPAM. Therefore, some Hawaiians are Californians.

Valid

Determine whether each argument is valid or invalid: All birds can fly. Oscar is a bird. Therefore, Oscar can fly.

Valid

Determine whether each argument is valid or invalid: All dogs go to heaven. Shadow is a dog. Therefore, Shadow will go to heaven.

Valid

Determine whether each argument is valid or invalid: It always snows when it is cold. It is cold. Therefore, it is snowing.

1. Statement 2. Contrapostive 3. Inverse 4. Converse

For the statement R→S, identify the Inverse, Converse, Contrapositive and original statement. 1. R → S 2. ~S → ~R 3. ~R → ~S 4. S → R

ad hominem

It was his fault, Officer. You can tell by the kind of car I'm driving and by my clothes that I am a good citizen and would not lie. Look at the rattletrap he is driving, and look at how he is dressed. You can't believe anything that a dirty, longhaired hippie like that might tell you. Search his car; he probably has pot in it.

ad hominem

John Bardeen's work at the Advanced Institute for Physics has progressed so slowly that even his colleagues call him a plodder. Hence, it is prudent at present not to take seriously his current theory relating how strings constitute the smallest of subatomic particles.

appeal to consequence

John has really worked hard on his term project, and he will really be depressed if he does not make an A. For these reasons, you just have to give him an A on his project.

True

Let A = {1, 4, 5, 7, 10}. Indicate if the statement is true or false. 5 ∈ A

1. {8,9,12,20} 2. {10,11,14}

Let S be the universal set, where: S={1,2,3,...,18,19,20} Let sets A and B be subsets of S, where: Set A = {1,5,6,7,8,9,12,19,20} Set B = {1,5,6,7,10,11,14,19} 1. (A ∩ B') = {____________} 2. (B ∩ A') = {____________}

1. {1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,19} 2. {13}

Let S be the universal set, where: S={1,2,3,...,18,19,20} Let sets A and B be subsets of S, where: Set A= {2,5,6,8,13,16,17,19} Set B={1,3,4,7,9,10,13,17,18,19} Set C={8,12,13,14,15,16} 1. (A ∪ B ∪ C) = {__________} 2. (A ∩ B ∩ C) = {____________}

appeal to consequence

My client is an integral part of this community. If he is sent to prison not only will this city suffer but also he will be most missed by his family. You surely cannot find it in your hearts to reach any other verdict than "not guilty."

ad hominem

Old man Brown claims that he saw a flying saucer in his farm, but he never got beyond the fourth grade in school and can hardly read or write. He is completely ignorant of what scientists have written on the subject, so his report cannot possibly be true.

c. If you are having pudding, then you ate your meat.

Select the contrapositive of: If you don't eat your meat, you can't have any pudding. a. If you eat your meat, then you can't have any pudding. b. If you can't have any pudding, then you didn't eat your meat. c. If you are having pudding, then you ate your meat. d. If you eat your meat, then you can have some pudding. e. Eat your meat or you can't have any pudding.

e. If you can't have any pudding, then you didn't eat your meat.

Select the converse of: If you don't eat your meat, you can't have any pudding. a. If you don't eat your meat, then you can have some pudding. b. Eat your meat or you can't have any pudding. c. If you are having pudding, then you ate your meat. d. If you eat your meat, then you can have some pudding. e. If you can't have any pudding, then you didn't eat your meat. f. If you eat your meat, then you can't have any pudding.

f. If you eat your meat, then you can have some pudding.

Select the inverse of: If you don't eat your meat, you can't have any pudding. a. If you can't have any pudding, then you didn't eat your meat. b. Eat your meat or you can't have any pudding. c. If you eat your meat, then you can't have any pudding. d. If you don't eat your meat, then you can have some pudding. e. If you are having pudding, then you ate your meat. f. If you eat your meat, then you can have some pudding.

Jim did not go to the store or Sally did go out.

Select the negation of: Jim went to the store and Sally did not go out.

Sears is not having a sale and I will not shop at Macy's.

Select the negation of: Sears is having a sale or I will shop at Macy's.

All jokes are not offensive.

Select the negation of: Some jokes are offensive.

a. Some dogs are cats.

Select the negation of: No dogs are cats. a. Some dogs are cats. b. Some dogs are not cats. c. All dogs are cats.

a. Some dogs do not go to heaven.

Select the negation of: All dogs go to heaven. a. Some dogs do not go to heaven. b. No dogs go to heaven. c. Some dogs go to heaven.

b. Sometimes I get a headache when I drink coffee.

Select the negation of: I never get a headache when I drink coffee. a. I always get a headache when I drink coffee. b. Sometimes I get a headache when I drink coffee. c. Sometimes I do not get a headache when I drink coffee.

a. No dogs go to heaven.

Select the negation of: Some dogs go to heaven. a. No dogs go to heaven. b. All dogs go to heaven. c. Some dogs do not go to heaven.

b. No horses run.

Select the statement that best describes the relationship depicted above: a. If it doesn't run, then it is not a horse. b. No horses run. c. All horses run. d. Some horses run. e. If it is not a horse, then it runs. f. If it is a horse, then it runs.

correlation implies causation

Since the 1950s, both the atmospheric carbon dioxide level and obesity levels have increased sharply. Hence, atmospheric carbon dioxide causes obesity.

Therefore, no sailors are miserly.

Supply a conclusion to make each argument valid: All sailors are big spenders. No big spenders are miserly.

Therefore, Bill will go to the movies

Supply a conclusion to make each argument valid: Bill will go to the movies or Sam will play golf. Sam does not play golf.

Therefore, if you pass the exam, then you can sell your book

Supply a conclusion to make each argument valid: If you pass the exam, then you will pass the course. If you pass the course, then you can sell your book.

Therefore, it did not snow

Supply a conclusion to make each argument valid: If it snows, then the ballgame will be rescheduled. The ballgame is not rescheduled.

Therefore, all flowers are tasty.

Supply a conclusion to make each argument valid: All flowers smell good. All things that smell good are tasty.

a. 19 b. 7 c. 6

The Venn diagram here shows the cardinality of each set. Use this to find the cardinality of each given set. a. n(A) = b. n(A∩C) = c. n(A∩B∩C') =

Fallacy of the Converse (Invalid)

Valid or Invalid

Fallacy of the Inclusive Or (Invalid)

Valid or Invalid

Fallacy of the Inverse (Invalid)

Valid or Invalid

Law Of Detachment (Valid)

Valid or Invalid

Law of Contraposition (Valid)

Valid or Invalid

Law of Disjunctive Syllogism (Valid)

Valid or Invalid

Law of Syllogism (Valid)

Valid or Invalid

false dilemma

We can go to the amusement park or the library. The amusement park is too expensive, so we must go to the library.

b. Some dogs do not go to heaven.

Which of the following is a quantified statement? a. Go, Eagles! b. Some dogs do not go to heaven. c. Go, Lions! d. That tasted great! e. If I had a hammer, I'd pound some nails.

e. Some flowers smell nice.

Which of the following is a quantified statement? a. If I had a hammer, I'd pound some nails. b. The Sun revolves around the Earth. c. The Mississippi River is the longest river in the world. d. Go, Tigers! e. Some flowers smell nice.

a. No movies are too long.

Which of the following is a quantified statement? a. No movies are too long. b. Honey is sweeter than sugar. c. That tasted terrible! d. Life is like a box of chocolates. e. Wild animals need to be protected.

a. Some dogs are beagles.

Which of the following is a quantified statement? a. Some dogs are beagles. b. Misery loves company. c. Whoa, Nelly! d. Go, Tigers! e. The Aztec empire was in what is now Mexico.

appeal to authority

You will tell the general manager that I made the right choice in dealing with that customer. After all, I'm the shift manager, so my decisions are always right.

12

n(A'∩B') =