PHL 111 Quiz 1
Find a Counterexample: No cars are buses. No cars are trucks. Therefore, no trucks are buses.
C = pigs, B = reptiles, and T = snakes.
Find a Counterexample: No cars are buses. No cars are trucks. Therefore, no trucks are buses.
No C are B. No C are T. No T are B.
It follows from the fact that she eats pork, chicken, beef, mutton, veal, venison, turkey, and fish that she must not be a vegetarian.
Argument
More damage was done last year from hurricanes than earthquakes. There was $100 million damage last year from hurricanes. There was $70 million damage last year from earthquakes.
Argument
My car won't start. But I just had it tuned up yesterday. So, that mechanic must be incompetent.
Argument
Find a Counterexample: No squares are circles. No triangles are circles. It follows that no squares are triangles.
No S are C. No T are C. No S are T.
Every statement is either true or false; these two possibilities are called truth values.
True
If a passage expresses a reasoning process, then it makes an inferential claim.
True
An invalid argument is automatically an unsound argument.
True
Computers will soon be in every home because the cost of buying one goes down dramatically every year.
Argument
Find a Counterexample: No cars are trucks. No trucks are buses. Therefore, no buses are cars.
C = mammals, T = snakes, and B = dogs.
Every fish has gills. I have twenty fish in my aquarium. It follows that all the fish in my aquarium have gills.
Deductive
Every horse can run a mile in under 3 minutes. Evie has a horse. Therefore, Evie's horse can run a mile in under three minutes.
Deductive
Jim was born in July. It follows necessarily that Jim was not born in December.
Deductive
Only those with tickets can enter the theater. You don't have a ticket. So, you can't enter the theater.
Deductive
There has been an overall decrease in violence among humans worldwide throughout recorded history. Biologically speaking, this is because the genetic characteristics for nonviolence have been selected over time by the species.
Explanation
A counterexample to an argument is evidence that the conclusion is false.
False
A deductive argument is one in which it is claimed that the conclusion follows probably from the premises.
False
An argument is any group of statements.
False
An argument must have at least two premises.
False
An inductive argument is cogent when the argument is strong, even if the premises are false
False
Some motorcycles are not fast machines. Lou owns a motorcycle. So, Lou's motorcycle is not a fast machine.
Inductive
The coin came up heads on the last toss. It probably will come up tails on the next toss.
Inductive
The exam's range of C scores is 70-79. I got a C on the exam. Therefore, maybe I got a 75 on the exam.
Inductive
If Katie really has a crush on you, then why didn't she text you last night?
Katie didn't text you last night [Katie does not have a crush on you]
If Trey enjoys cricket, Trey enjoys quiet activities. Trey dosen't enjoy quiet activities. Thus, Trey doesn't enjoy cricket.
Modus Tollens
Find a Counterexample: No cars are buses. No cars are trucks. Therefore, no trucks are buses.
No C are B. No C are T. No T are B.
Find a Counterexample: No cars are trucks. All trucks are heavy equipment. Therefore, no cars are heavy equipment.
No C are T. All T are H. No C are H.
Find a Counterexample: No cars are trucks. No trucks are buses. Therefore, no cars are buses.
No C are T. No T are B. No C are B.
Most scientists agree that global warming is caused by human activity.
Not an argument
The stock market has gone down for the last 3 weeks. It will probably go down again next week.
Weak
There are thirty students in my class. Two students got a perfect score on the last exam. I am probably one of the students who got a perfect score on the last exam.
Weak
Alison's pet is vicious Alison's pet is a dog *Alison's pet weighs less than 2lbs
Weakens
I got at least a 95 on all my exams in this course. The syllabus says that anything over a 92 is an A. So, I expect to get an A for the course.
Argument
Alison's pet is vicious Alison's pet is a dog *Alison's pet is a mammal
Strenghtens
Our college football team lost by 30 points yesterday. The quarterback must not have played in the game.
Explanation
She quit her job today because she inherited $1 million from a rich relative
Explanation
A proposition is the information content imparted by a statement, or, simply put, its meaning.
True
The exam's range of C scores is 70-79. I got a C on the exam. Therefore, maybe I got a 75 on the exam.
Weak
Only a few people will be chosen for the Olympic team. John will make the Olympic team.
Weak
Not all vegetables contain antioxidants. All we're having for dinner tonight are artichokes. Artichokes are a vegetable. So, our dinner tonight will not contain antioxidants.
Inductive
Anyone over 18 years of age can join the military. Linda is 19 years old. Thus, Linda can join the military.
Deductive
Every apple grows on trees. I am eating an apple, so I am eating something that grew on a tree.
Deductive
A counterexample to a statement is evidence that shows the statement is false.
True
Jane was born in a leap year. She was probably born on February 29.
Weak
The exam's range of C scores is 70-79. I got a 98 on the exam. Therefore, I did not get a C on the exam.
Deductive
Alison's pet is vicious Alison's pet is a dog *Alison's pet has four legs
Strengthens
Building fuel-efficient cars helps reduce gasoline consumption. Dependency on foreign oil for gasoline production is a drain on the economy. Offshore oil drilling is dangerous. Oil spills through faulty drilling are hazardous to life; so are large tanker spills. Carbon emissions are hurting the environment. We need to start building more fuel-efficient cars. *Carbon emissions are hurting the environment.*
Premise
Only a few people will be chosen for the Olympic team. Of those receiving phone calls from the selection committee, 80% will make the team. John received a phone call from the selection committee. John will probably make the Olympic team.
Strong
We should stop interfering in other countries' affairs. This follows from the fact that we have no moral right to change a country's way of governing itself. Also, interfering often gets us locked into combat; not to mention that the potential for loss of lives on both sides is high. In addition, the cost of waging wars is astronomical. Any engagement means weakening our already shaky economy. Add the fact that interfering makes us have more enemies around the world who feel threatened by us. *We should stop interfering in other countries' affairs.*
Conclusion
Most apples are red. I am eating an apple. So I am eating something red.
Inductive
Find a Counterexample: All squares are triangles. All triangles are circles. Therefore, all circles are squares.
S = puppies, T = dogs, and C = mammals.
Newspapers are a good source of in-depth news and they are easily accessible. Weekly magazines are good source of in-depth news and they are easily accessible. PBS, CNN, and CSPAN are good sources of in-depth news and they are easily accessible. There is no reason why anyone should remain ignorant of what's going on in the world.
Argument
She just ate two plates of nachos. She always gets sick after she eats so much. I bet she gets sick later tonight.
Argument
All elements with atomic weights less than 50 are unstable. Q is an element with an atomic weight of 49. Therefore, Q is unstable.
Deductive
A single counterexample to a deductive argument is enough to show that an argument is invalid.
True
He was born in 1988. According to the Chinese zodiac, that happens to be a Dragon year. Thus, he is sure to have good fortune all his life.
Argument
Find a Counterexample: All rectangles are squares. All rectangles are parallelograms. Therefore, all parallelograms are squares.
R = puppies, S = dogs, and P = mammals
Find a Counterexample: No squares are triangles. No squares are circles. Therefore, no triangles are circles.
S = motorcycles, T = cats, and C = mammals.
Paris is called the "City of Lights." Las Vegas is also called the "City of Lights." So, there must be at least two cities with the same nickname. *There must be at least two cities with the same nickname.*
Conclusion
An inductive argument is uncogent only when the argument is weak.
False
Find a Counterexample: All squares are rectangles. All squares are parallelograms. It follows that all rectangles are parallelograms.
S = puppies, R = mammals, and P = dogs.
Most earthquakes do considerable damage to infrastructure when the earthquake occurs near a large city. There was an earthquake today near a large city in South America. There will probably be considerable damage to infrastructure.
Strong
Most people over 18 are registered to vote. Lisa is 19 years old. So, Lisa is registered to vote.
Strong
Find a Counterexample: All squares are parallelograms. All rectangles are parallelograms. Therefore, all squares are rectangles.
All S are P. All R are P. All S are R.
Find a Counterexample: All squares are triangles. All triangles are circles. Therefore, all circles are squares.
All S are T. All T are C. All C are S.
Every horse can run a mile in under 3 minutes. Evie has a pet that can run a mile in under 3 minutes. Therefore, Evie's pet is a horse.
Inductive
Jim was born in the summer. So perhaps he was born in July.
Inductive
My aunt invested $1000 in the stock market last month. The TV announcer said that the average stock has lost 20% in value this month. I guess we know what that means. My aunt probably lost $250 in stock value.
Argument
My brother is going to make a lot of money. Phone apps are big business. Some apps are expensive. Of course, others cost a lot. My brother is creating some new games that he will market as apps.
Argument
Since there is biological evidence that the genetic characteristics for nonviolence have been selected over time by the species, we should see an overall decrease in violence among humans worldwide in the coming centuries.
Argument
Hamburgers are loaded with saturated fat and sodium. Pizza is loaded with saturated fat and sodium. Too much saturated fat and sodium is harmful to your heart. Jim takes in too much saturated fat and sodium. It follows Jim is harming his heart. *Jim is harming his heart.*
Conclusion
Paris's Eiffel Tower is three times as tall as the one in Las Vegas. The Luxor Pyramid in Las Vegas is half the size of the original in Egypt. The Statue of Liberty in New York is four times the one in Las Vegas. Thus, every object in Las Vegas is smaller than in other cities. *Every object in Las Vegas is smaller than in other cities.*
Conclusion
All motorcycles are fast machines. Lou owns a motorcycle. So, Lou's motorcycle is a fast machine.
Deductive
Some citizens prefer to live overseas. My uncle lives overseas. Thus, my uncle is a citizen.
Deductive
If Gerry wins the election, Mary loses the election. Gerry does not win the election. So, Mary does not lose the election.
Denying the Antecedent
My car won't start. I must be out of gas.
Explanation
An inductive argument is one in which it is claimed that the conclusion follows necessarily from the premises.
False
Since Herb is a nervous driver he won't want to come with us on this parachute jump.
Herb is a nervous driver [Most people who are nervous drivers are people who would not like to go on parachute jumps] Herb won't want to come with us on this parachute jump
Mary was born on August 12. Mike was born in August, too. There is little chance that Mike was born on the same day as Mary.
Inductive
Most elements with atomic weights less than 50 are unstable. Q is an element with an atomic weight of 49. Therefore, Q is unstable.
Inductive
Most sea creatures have gills. Dolphins are sea creatures. Dolphins probably have gills.
Inductive
I like candy. I love chocolate. I hate peanuts. Also, I don't care for circus acts or water sports. It's OK if you like that stuff.
Not an argument
Our teacher is funny. She is also helpful. I believe she is a full professor.
Not an argument
Building fuel-efficient cars helps reduce gasoline consumption. Dependency on foreign oil for gasoline production is a drain on the economy. Offshore oil drilling is dangerous. Oil spills through faulty drilling are hazardous to life; so are large tanker spills. Carbon emissions are hurting the environment. We need to start building more fuel-efficient cars. *Building fuel-efficient cars helps reduce gasoline consumption.*
Premise
Building fuel-efficient cars helps reduce gasoline consumption. Dependency on foreign oil for gasoline production is a drain on the economy. Offshore oil drilling is dangerous. Oil spills through faulty drilling are hazardous to life; so are large tanker spills. Carbon emissions are hurting the environment. We need to start building more fuel-efficient cars. *Large tanker spills are hazardous to life.*
Premise
Hamburgers are loaded with saturated fat and sodium. Pizza is loaded with saturated fat and sodium. Too much saturated fat and sodium is harmful to your heart. Jim takes in too much saturated fat and sodium. It follows Jim is harming his heart.
Premise
Hamburgers are loaded with saturated fat and sodium. Pizza is loaded with saturated fat and sodium. Too much saturated fat and sodium is harmful to your heart. Jim takes in too much saturated fat and sodium. It follows Jim is harming his heart. *Pizza is loaded with saturated fat and sodium.*
Premise
Hamburgers are loaded with saturated fat and sodium. Pizza is loaded with saturated fat and sodium. Too much saturated fat and sodium is harmful to your heart. Jim takes in too much saturated fat and sodium. It follows Jim is harming his heart. *Too much saturated fat and sodium is harmful to your heart.*
Premise
Paris is called the "City of Lights." Las Vegas is also called the "City of Lights." So, there must be at least two cities with the same nickname. *Las Vegas is also called the "City of Lights."*
Premise
Paris is called the "City of Lights." Las Vegas is also called the "City of Lights." So, there must be at least two cities with the same nickname. *Paris is called the "City of Lights."*
Premise
Soy bean curd has no taste. The fat in hamburgers is what gives them their great taste. The fat in pizza is what gives it great taste. Food without fat tastes bland. Soy bean curd has no fat. *The fat in pizza is what gives it great taste.*
Premise
We should stop interfering in other countries' affairs. This follows from the fact that we have no moral right to change a country's way of governing itself. Also, interfering often gets us locked into combat; not to mention that the potential for loss of lives on both sides is high. In addition, the cost of waging wars is astronomical. Any engagement means weakening our already shaky economy. Add the fact that interfering makes us have more enemies around the world who feel threatened by us. *Interfering makes us have more enemies around the world who feel threatened by us.*
Premise
We should stop interfering in other countries' affairs. This follows from the fact that we have no moral right to change a country's way of governing itself. Also, interfering often gets us locked into combat; not to mention that the potential for loss of lives on both sides is high. In addition, the cost of waging wars is astronomical. Any engagement means weakening our already shaky economy. Add the fact that interfering makes us have more enemies around the world who feel threatened by us. *Interfering often gets us locked into combat.*
Premise
We should stop interfering in other countries' affairs. This follows from the fact that we have no moral right to change a country's way of governing itself. Also, interfering often gets us locked into combat; not to mention that the potential for loss of lives on both sides is high. In addition, the cost of waging wars is astronomical. Any engagement means weakening our already shaky economy. Add the fact that interfering makes us have more enemies around the world who feel threatened by us. *The cost of waging wars is astronomical.*
Premise
Most apples are red. I am eating an apple. So I am eating something red.
Strong
Most elements with atomic weights less than 50 are unstable. Q is an element with an atomic weight of 49. Therefore, Q is unstable.
Strong
Most horses can run a mile in under 3 minutes. Evie has a horse. Therefore, Evie's horse probably can run a mile in under 3 minutes.
Strong
Only a few strawberries in that container are sour. The strawberry you picked from that container is probably not sour.
Strong
An invalid deductive argument is one where, assuming the premises are true, it is possible for the conclusion to be false.
True
Leo makes only $10 an hour waiting tables part time. He probably is not able to save even $5 a week from his paycheck.
Weak
Robert is a senior citizen. Therefore, he is probably over 90 years of age.
Weak
