Intro to Logic HW & Quizzes

What most accurately depicts the form of the following? All dragons who are friendly are users of illegal drugs. A. All D who are F are U B. No D who are F are U C. All F who are not F are not U D. All D are F and U

A. All D who are F are U

On the basis of the previous question, what can one correctly conclude about all arguments with the following form? Some people are smart. Some people are women. Therefore, some people are smart women. Note that there might be more than one correct answer! A. All arguments of the form are invalid. B. All arguments of the form are valid, but unsound. C. All arguments of the form are unsound D. All arguments of the form are valid.

A. All arguments of the form are invalid. & C. All arguments of the form are unsound EXPLANATION: (Correct! All arguments with the same form are either valid or invalid if any argument of that form is valid or invalid. All arguments with the same form are either valid or invalid if any argument of that form is valid or invalid. Since the argument is invalid, it is unsound: an argument can be sound only if it is valid! (Remember: an argument is sound iff it is valid.))

Which answer is this an instance of? A ⊃ (B ∨ C) A. If Annie wins, then either Ben runs or Cindy sings. B. It's either the case that if Annie wins then Ben runs or Cindy sings.

A. If Annie wins, then either Ben runs or Cindy sings.

Here is an argument: (P1) If it is raining, then we will not go outside. (P2) It is raining, (C) So, we will not go outside. Which of the following statements mostly closely shares the form of (P1)? A. If it snowing, then it is not the case that we will wear shorts. B. If it is raining, then will will go play in the mud. C. If it is snowing, then we will have hot chocolate. D. It is either raining or it is not raining.

A. If it snowing, then it is not the case that we will wear shorts. EXPLANATION: (That's right. The form of (P1) is: If P, then not-Q. The form of "If it is snowing, then it is not the case that we will wear shorts" is: If R, then not-S, since "it is not the case" has the same meaning as "not".)

"Implies" is correctly symbolized with the horseshoe symbol. A. True B. False

A. True

"Therefore," "for that reason," "hence," and "thus" are conclusion-indicator words. A. True B. False

A. True

All statements are either true or false. A. True B. False

A. True

Answer 'true' or 'false': An argument's conclusion is the claim that the argument is an argument for. A. True B. False

A. True

Answer 'true' or 'false': Premises provide support for an argument's conclusion. A. True B. False

A. True

True or false In biconditionals, the main operator is a triple bar. A. True B. False

A. True

P provided that Q is correctly symbolized as Q ⊃ P. A. True B. False

A. True EXPLANATION: (That's right. The claim being made is that if Q, then P. So, we symbolize this Q ⊃ P.)

How is the following correctly symbolized? Either you won't pass, or you will get an A. A. ~ P ∨ A B. ~ (P ∙ C. ~ (P ∨ A) D. ~ P ⊃ A

A. ~ P ∨ A

Translate the following into symbolic form: Neither Ferrari nor Maserati makes economy cars. A = Ferrari makes economy cars. B = Maserati makes economy cars. A. ~A ∙ ~B B. A ∨ ~B C. A ∙ B D. ~(A ≡ B)

A. ~A ∙ ~B

How is the following correctly symbolized? It is not snowing. A. ~S B. LaTeX: \bullet S

A. ~S

INSTRUCTIONS: The following selections relate to distinguishing arguments from nonarguments and identifying conclusions. Select the best answer for each. Humans are biological organisms. To understand our behavior and mental processes, we need to understand their biological underpinnings, starting with the cellular level, the neuron. How we feel, learn, remember, and think all stem from neuronal activity. So, how a neuron works and how neurons communicate are crucial pieces of information in solving the puzzle of human behavior and mental processing. Richard Griggs, Psychology: A Concise Introduction

Argument; conclusion: How a neuron works ... mental processing.

INSTRUCTIONS: The following selections relate to distinguishing arguments from nonarguments and identifying conclusions. Select the best answer for each. It is likely that innocent prisoners in this country have been executed for crimes they did not commit. From 1973 until 2016, 151 death row inmates have been exonerated. In many of these cases DNA evidence played a crucial role. Yet, in that same time frame, more than 1000 prisoners were executed. For many of these prisoners no DNA evidence was available. If such evidence had been available, how may more would have been exonerated? Correct!

Argument; conclusion: It is likely that innocent prisoners ... they did not commit.

INSTRUCTIONS: The following selections relate to distinguishing arguments from nonarguments and identifying conclusions. Select the best answer for each. Undocumented immigrants pay local sales taxes, and many of them also pay state, local, and federal income tax and Social Security tax. They also purchase items from local merchants, increasing the amount these merchants pay in taxes. In addition, they work for low salaries, which increases the earnings of their employers and the amount of taxes these employers pay. Thus, it is not correct to say that undocumented immigrants contribute nothing to the communities in which they live.

Argument; conclusion: It is not correct to say ... communities in which they live.

INSTRUCTIONS: The following selections relate to distinguishing arguments from nonarguments and identifying conclusions. Select the best answer for each. The earth is of interest to astronomy for many reasons. Nearly all observations must be made through the atmosphere, and the phenomena of the upper atmosphere and the magnetosphere reflect the state of interplanetary space. The earth is also the most important object of comparison for planetologists. Hannu Karttunen, et al., Fundamental Astronomy

Argument; conclusion: The earth is of interest to astronomy.

We will go to the picnic iff it is not raining and it is warm. A= We will go to the picnic B = It is raining C = It is warm A. (A ≡ B) ∙ C B. A ≡ (~ B ∙ C) C. A ≡ ~ B ∙ C

B. A ≡ (~ B ∙ C)

If ISIS is defeated, then many people will be happy, but the terrorists won't be happy. A = ISIS is defeated B = Many people will be happy C = The terrorists will be happy A. A ⊃ B ∙ ~ C B. A ⊃ (B ∙ ~ C) C. (A ∙ B) ⊃ ~ C

B. A ⊃ (B ∙ ~ C)

Which of the following is the definition of "validity"? A. An argument is valid iff its premises are true. B. An argument is valid iff it is not possible for its premises to be true and its conclusion false at the same time. C. An argument is valid iff its premises and conclusion are true.

B. An argument is valid iff it is not possible for its premises to be true and its conclusion false at the same time.

The following is an argument. Which of the statements is the conclusion? Economics is of practical value in business. An understanding of the overall operation of the economic system puts the business executive in a better position to formulate policies. The executive who understands the causes and consequences of inflation is better equipped during inflationary periods to make more-intelligent decisions than otherwise. A. An understanding of the overall operation of the economic system puts the business executive in a better position to formulate policies. B. Economics is of practical value in business. C. The executive who understands the causes and consequences of inflation is better equipped during inflationary periods to make more-intelligent decisions than otherwise.

B. Economics is of practical value in business. EXPLANATION: (The rest of the paragraph gives reasons for thinking that economics is of practical value in business.)

True or false? The following is a well-formed formula: ~(K ∨ L) ∙ A ( ⊃ G ∨ H) A. True B. False

B. False

If an argument is valid and has true premises, then it is A. Strong B. Sound C. Merely Valid

B. Sound EXPLANATION: (That's correct. Remember, an argument is sound iff it is valid and its premises are true.)

INSTRUCTIONS: Select the correct translation for each problem. Carnival advertises its parties if and only if Disney's promoting family cruises implies that Norwegian improves its entertainment. A. (C ≡ D) ⊃ N B. (C ⊃ D) • (N ⊃ C) C. C ≡ (D ⊃ N) D. C ⊃ (D ≡ N) E. C ≡ (N ⊃ D)

C. C ≡ (D ⊃ N)

Proposition 2D Given the following proposition: [(A • ∼ X) ⊃ (∼ B ≡ Y)] • [∼ (Y ∨ ∼ A) ≡ (B • X)] In Proposition 2D, the main operator is a: A. Wedge. B. Horseshoe. C. Dot. D. Tilde. E. Triple bar.

C. Dot.

The following is an argument. Which statement is its conclusion? Freedom of the press is the most important of our constitutionally guaranteed freedoms. Without it, our other freedoms would be immediately threatened. Furthermore, it provides the fulcrum for the advancement of new freedoms. A. Without it, our other freedoms would be immediately threatened. B. Furthermore, it provides the fulcrum for the advancement of new freedoms. C. Freedom of the press is the most important of our constitutionally guaranteed freedoms.

C. Freedom of the press is the most important of our constitutionally guaranteed freedoms. EXPLANATION: (That's right. This passage seeks to convince us that freedom of the press is especially important, and then it gives us some reasons for thinking that that is the case. That's what the other statements do: they provide evidence for the first sentence's truth.)

Here is an argument: (P1) If it is misty, then we will not go rowing. (P2) It is misty, (C) So, we will not go rowing. Which of the following statements mostly closely shares the form of (P1)? A. If it is raining, then will will go play in the mud. B. If it is snowing, then we will have hot chocolate. C. If it snowing, then it is not the case that we will wear shorts. D. It is either raining or it is not raining.

C. If it snowing, then it is not the case that we will wear shorts. EXPLANATION: (That's right. The form of (P1) is: If P, then not-Q. The form of "If it is snowing, then it is not the case that we will wear shorts" is: If R, then not-S, since "it is not the case" has the same meaning as "not".)

Proposition 1A Given the following proposition: [A ⊃ ∼ (B • Y)] ≡ ∼[B ⊃ (X • ∼ A)] In Proposition 1A, the main operator is a: A. Triple bar. B. Wedge. C. Triple bar. D. Dot. E. Horseshoe.

C. Triple bar.

Proposition 1F Given the following proposition: ∼ [∼ (X ∨ ∼ Y) ≡ (∼ X ⊃ ∼A)] ∨ ∼ (B • ∼ A) In Proposition 1F, the main operator is a: A. Dot. B. Horseshoe. C. Wedge. D. Tilde. E. Triple bar.

C. Wedge.

Which most accurately depicts the form of the following? All doggos who are fluffy are good. A. No D who are F are G B. All D are F and G C. All F who are not F are not G D. All D who are F are G

D. All D who are F are G EXPLANATION: (Good. Make sure to keep the logical constants the same throughout.)

How is the following correctly symbolized? If it is cold, then you will wear a coat. A. C ~ (W) B. C ∙ C. C ∨ W D. C ⊃ W

D. C ⊃ W

Proposition 2A Given the following proposition: [(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃ X)] In Proposition 2A, the main operator is a: A. Wedge. B. Tilde. C. Dot. D. Horseshoe. E. Triple bar.

D. Horseshoe.

Proposition 1E Given the following proposition: ∼{[(Y ≡ ∼ A) ⊃ (∼ X ∨ Y)] • (∼ B ∨ ∼ X)} In Proposition 1E, the main operator is a: A. Dot. B. Triple bar. C. Wedge. D. Tilde. E. Horseshoe.

D. Tilde.

Proposition 2B Given the following proposition: [(A ⊃ Y) ≡ (B ⊃ ∼X)] ∨ ∼[(B • ∼ X) ≡ (Y • A)] In Proposition 2B, the main operator is a: A. Horseshoe. B. Dot. C. Tilde. D. Wedge. E. Triple bar.

D. Wedge.

Proposition 1B Given the following proposition: ∼[(A ∨ ∼ B) ⊃ X] ⊃ [∼ Y ⊃ (A • X)] In Proposition 1B, the main operator is a: A. Dot. B. Triple bar. C. Wedge. D. Tilde. E. Horseshoe.

E. Horseshoe.

Proposition 2F Given the following proposition: [(X ⊃ ∼ Y) • ∼ (X ∨ ∼ B)] ⊃ [∼ (B ⊃ ∼ Y) ≡ (A • ∼ Y)] In Proposition 2F, the main operator is a: A. Triple bar. B. Dot. C. Tilde. D. Wedge. E. Horseshoe.

E. Horseshoe.

Proposition 1D Given the following proposition: ∼ (A • ∼ X) ≡ [A ⊃ (Y ∨ ∼ B)] In Proposition 1D, the main operator is a: A. Tilde. B. Wedge. C. Horseshoe. D. Dot. E. Triple bar.

E. Triple bar.

Proposition 2E Given the following proposition: [∼ (A ∨ Y) ≡ (∼ X ⊃ B)] ∨ [∼ (Y • ∼ B) ⊃ (X ⊃ ∼ A)] In Proposition 2E, the main operator is a: A. Horseshoe. B. Dot. C. Tilde. D. Triple bar. E. Wedge.

E. Wedge.

I am required to take the final exam for this course in person and not on Carmen.

False

Late assignments are no big deal, and the instructor will accept them no questions asked.

False

Proposition 1B Given the following proposition: ∼[(A ∨ ∼ B) ⊃ X] ⊃ [∼ Y ⊃ (A • X)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 1B.

False

Proposition 1E Given the following proposition: ∼{[(Y ≡ ∼ A) ⊃ (∼ X ∨ Y)] • (∼ B ∨ ∼ X)} Given that A and B are true and X and Y are false, determine the truth value of Proposition 1E.

False

Proposition 2A Given the following proposition: [(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃ X)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 2A.

False

Proposition 2D Given the following proposition: [(A • ∼ X) ⊃ (∼ B ≡ Y)] • [∼ (Y ∨ ∼ A) ≡ (B • X)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 2D.

False

Proposition 2F Given the following proposition: [(X ⊃ ∼ Y) • ∼ (X ∨ ∼ B)] ⊃ [∼ (B ⊃ ∼ Y) ≡ (A • ∼ Y)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 2F.

False

True/false: The BOLDED portion of the following conditional statement is the antecedent of the conditional statement. If today is Sunday, then YOUR QUIZ IS DUE TODAY.

False

True/false: The BOLDED portion of the following conditional statement is the antecedent of the conditional statement. If today is Saturday, then YOUR QUIZ IS DUE TOMORROW.

False

There are arguments with no conclusions.

False EXPLANATION: (All arguments have conclusions. Remember: arguments have conclusions because they are collections of statements which are taken to support another of them, the conclusion.)

True/False: To determine if an argument is valid, you must know whether its premises are actually true or false.

False EXPLANATION: (Good. To determine if an argument is valid, you don't need to know whether the premises are true or false. Instead, all you need to figure out is whether, if the premises the premises are true, the conclusion must also be true.)

True/False: The following argument is valid. (P1) All lawyers are women. (P2) Suzanne is a woman. (C) Therefore, Suzanne is a lawyer.

False EXPLANATION: (Imagine that the premises are true. Then we know that all lawyers are women and that Suzanne is a woman. It doesn't follow, though, that Suzanne is a lawyer: for that to follow from the premises with certainty, we would need to know that Suzanne is a lawyer. Another way to think about it is that, it might be true that all lawyers are women and that Suzanne is a woman. But it wouldn't follow that Suzanne is a lawyer. She might be a doctor or astronaut, for instance.)

True/False: The counterexample/countermodel method can be used to prove that an argument form is valid.

False EXPLANATION: (It can only be used to prove that an argument form is invalid because "the only arrangement of truth and falsity that proves anything is true premises and false conclusion. If a substitution instance is produced having true premises and a true conclusion, it does not prove that the argument is valid." (H&W 65). This is because there may be instances of the argument where the premises are true and the conclusion false; but a single instance of such an argument does not prove that the argument is valid. Consider, for instance, the argument in the previous question: Some people are smart. Some people are women. Therefore, some people are smart women. It is certainly an argument with true premises and a true conclusion, but it is not, as we've seen, valid. So a single instance of an argument form with true premises and a true conclusion cannot prove the argument is valid.)

An argument is valid if its premises are true.

False EXPLANATION: (Remember, an argument is valid iff it is not possible for its premises to be true and its conclusion false at the same time. Suppose an argument has true premises. This does not tell us whether the argument is valid or not. There can be invalid arguments with true premises. Consider the following one, for example: Columbus, Ohio is north of Cincinnati, Ohio. Cleveland, Ohio is north of Columbus, Ohio. Therefore, Cincinnati, Ohio is north of Cleveland, Ohio. This argument has true premises, but its conclusion is plainly false. Now, an argument is valid iff it is not possible for its premises to be true and its conclusion false at the same time. Therefore, this argument is invalid even though its premises are true. Thus, it is false that an argument is valid if its premises are true.)

True/False: To determine if an argument is valid, you need to know whether its premises are true.

False EXPLANATION: (Remember, an argument is valid iff its not possible for its premises to be true and its conclusion false at the same time. To determine if that's the case, you don't need to know if the premises are actually true or false. All you need to find out is whether if the premises are true, the conclusion has to be true as well.)

True/False: The following argument is valid. (P1) Some men are lawyers. (P2) Some lawyers are dishonest. (C) Therefore, some men are dishonest.

False EXPLANATION: (Suppose the premises are true. Then we know that some men are lawyers and some lawyers are dishonest. We don't know, however, that some men are dishonest. To see why, consider that the premises might be true while the conclusion is false: perhaps there are lawyers who are women, and that only women are dishonest. In that case, the premises would be true and the conclusion false. Now, we know that an argument is valid iff it is not possible for its premises to be true and its conclusion false at the same time. And an argument is invalid iff it is not valid. The premises could be true while the conclusion is false. Therefore, the argument is invalid.)

If an argument has a true conclusion, then it is valid.

False EXPLANATION: (That's correct. An argument is valid iff it is not possible for its premises to be true and its conclusion false at the same time. This tell us nothing about what happens if an argument has a true conclusion. For instance, here is an argument with a true conclusion that is invalid: If Trump is the President, then Pence is the Vice President. Pence is the Vice President. Therefore, Trump is the President. This argument is invalid, but it has a true conclusion. So, it is false that, if an argument has a true conclusion, then it is valid. To see that it is invalid, suppose that the premises are true. Must the conclusion also be true? Intuitively not: it might be the case that Pence is the Vice President, but someone other than Trump is the President.)

Some arguments are both sound and invalid.

False EXPLANATION: (That's correct. Consider the definition of "sound": An argument is sound iff (i) it is valid and (ii) its premises are true. If an argument is sound, then it follows that it is valid. Thus, there are no sound arguments that are invalid.)

Some valid arguments have true premises and a false conclusion.

False EXPLANATION: (That's correct. Remember, an argument is valid iff it is not possible for its premises to be true and its conclusion false at the same time. Suppose an argument is valid and its premises are true. By the definition above, we know that the argument must also have a true conclusion. Therefore, it is false that there are valid arguments with true premises and a false conclusion.)

There are valid arguments with true premises and a false conclusion.

False EXPLANATION: (That's correct. Remember, an argument is valid iff it is not possible for its premises to be true and its conclusion false at the same time. Suppose an argument is valid and its premises are true. By the definition above, we know that the argument must also have a true conclusion. Therefore, it is false that there are valid arguments with true premises and a false conclusion.)

Some arguments have no conclusion.

False EXPLANATION: (That's correct. Remember, an argument is a series of claims, some of which are designated as premises, and one of which is designated as the conclusion. So, all arguments must have a conclusion.)

To determine whether an argument is valid, you must know whether its premises are in fact true.

False EXPLANATION: (That's correct. To determine whether an argument is valid, you don't need to know whether its premises are actually true in the real world or not. Instead, you need to determine what would be the case if the premises are true: so imagine that the premises are true and ask yourself if the conclusion must also be true on the assumption that the premises are true.)

If an argument with a particular form is sound, then every argument with that same form is sound.

False EXPLANATION: (The counterexample/countermodel method can be used to show that an argument is invalid. However, it cannot be used to show that the premises of an argument are true. You might know that a particular argument form is valid and that a particular argument with that form is sound, but you don't thereby know of other arguments with that form whether their premises are true.)

True/False: The following is an argument. The turkey vulture is called by that name because its red, featherless head resembles the head of a wild turkey.

False EXPLANATION: (This is not an argument: it seeks to explain why something has the name it has, rather than providing support for some claim.)

True/False: The following is an argument. Lions at Kruger National Park in South Africa are dying of tuberculosis. "All of the lions in the park may be dead within ten years because the disease is incurable, and the lions have no natural resistance," said the deputy director of the Department of Agriculture.

False EXPLANATION: (This one is somewhat tricky. The quotation from the deputy director is an argument, but the entire passage isn't; its merely making a claim and then quoting someone who argues for that claim.)

True/False: The following is an argument. The sky appears blue from the earth's surface because light rays from the sun are scattered by particles in the atmosphere.

False EXPLANATION: (This passage seeks to explain why a certain fact obtains, namely why the sky appears blue from the earth's surface.)

Any argument with true premises and a true conclusion is sound.

False (That's right. The following is an argument with true premises and a true conclusion, but it is unsound because it is invalid: (P1) Either Trump is the President or Pence is the Vice President. (P2) Pence is the Vice President. (C) Therefore, Trump is the President. Each of the premises and conclusion is true, but the argument is invalid. To see why, note that each premise is true and the conclusion is true. But (P1) and (P2) would be true even if Pence were the Vice President and someone other than Trump is the President.)

INSTRUCTIONS: The following selections relate to distinguishing arguments from nonarguments and identifying conclusions. Select the best answer for each. If the trade in tiger products is banned, tiger reserves are guarded by well equipped staff, communities abutting tiger habitat are given a stake in protecting tigers, and the makers of traditional medicines can be persuaded that tiger parts are not needed, then tiger poaching will be halted, habitat and life sustaining prey will be restored, and the immanent extinction of tigers in the wild will be averted.

Nonargument.

INSTRUCTIONS: The following selections relate to distinguishing arguments from nonarguments and identifying conclusions. Select the best answer for each. Lead is toxic, but do you know why? Lead is toxic mainly because it preferentially replaces other metals in biochemical reactions. In so doing it interferes with the proteins that regulate blood pressure (which can cause development delays in children and high blood pressure in adults), heme production (which can lead to anemia), and sperm production. Lead also displaces calcium in the reactions that transmit electrical impulses in the brain, which diminishes the ability to think and recall information. Anne Marie Helmenstine, "Your Guide to Chemistry"

Nonargument.

Proposition 1A Given the following proposition: [A ⊃ ∼ (B • Y)] ≡ ∼[B ⊃ (X • ∼ A)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 1A.

True

Proposition 1D Given the following proposition: ∼ (A • ∼ X) ≡ [A ⊃ (Y ∨ ∼ B)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 1D.

True

Proposition 1F Given the following proposition :∼ [∼ (X ∨ ∼ Y) ≡ (∼ X ⊃ ∼A)] ∨ ∼ (B • ∼ A) Given that A and B are true and X and Y are false, determine the truth value of Proposition 1F.

True

Proposition 2B Given the following proposition: [(A ⊃ Y) ≡ (B ⊃ ∼X)] ∨ ∼[(B • ∼ X) ≡ (Y • A)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 2B.

True

Proposition 2E Given the following proposition:[∼ (A ∨ Y) ≡ (∼ X ⊃ B)] ∨ [∼ (Y • ∼ B) ⊃ (X ⊃ ∼ A)] Given that A and B are true and X and Y are false, determine the truth value of Proposition 2E.

True

To show that an argument form is invalid, one constructs a counterexample where an argument of the same form has true premises and a false conclusion.

True

True/False: The following argument is valid. All physicians are individuals who have earned degree in political science, and some lawyers are physicians. Therefore, some lawyers are person who have earned degrees in political science.

True

True/False: The following argument is valid. All physicians are individuals who have earned degree is in political science, and some lawyers are physicians. Therefore, some lawyers are person who have earned degrees in political science.

True

True/False: The following argument is valid. If Queen Elizabeth was born in Los Angeles, then she is a California native. Queen Elizabeth is not a California native. Therefore, Queen Elizabeth was not born in Los Angeles.

True

True/False: The following argument is valid. (P1) The Empire State Building is taller than the Statue of Liberty. (P2) The Statue of Liberty is taller than the Eiffel Tower. (C) Therefore, the Empire State Building is taller than the Eiffel Tower.

True

True/false: The BOLDED portion of the following conditional statement is the antecedent of the conditional statement. If TODAY IS SUNDAY, then your work is late.

True

All sound arguments have true premises and a true conclusion.

True EXPLANATION: (That's right. An argument is sound iff (i) it is valid and (ii) it has true premises. We know that, if an argument is valid, then if it's premises are true, then its conclusion must also be true. So suppose we have a sound argument. Then we know, by (ii) in the definition of "sound," that its premises are true. And we know by the definition of "valid" that, if a valid argument has true premises, that its conclusion must also be true. Therefore, we know that, if an argument is sound, then its premises and conclusion must all be true.)

The following is valid: Cincinnati, Ohio is north of Columbus, Ohio. Cleveland, Ohio is north of Cincinnati, Ohio. Therefore, Cincinnati, Ohio is north of Columbus, Ohio.

True EXPLANATION: (Although the first premise and the conclusion are false, this is a valid argument. It is not possible for the premises to be true and the conclusion false at the same time. To see this, suppose that the premises are true. The map of Ohio would look different, but the conclusion would follow from the premises! In fact, the conclusion just is the same as the first premise. So, if the first premise is true, then the conclusion must also be true.)

If an argument is sound, then it is valid.

True EXPLANATION: (That's correct. An argument is sound iff (i) it is valid and (ii) its premises are true. If an argument is sound, then it is ipso facto valid. Therefore, it is true that all sound arguments are valid.)

To determine whether a valid argument is sound, you must know whether its premises are in fact true.

True EXPLANATION: (That's correct. Remember, an argument is sound iff (i) it is valid and (ii) its premises are true. If you know that an argument is valid, you don't thereby know whether it is sound unless you have also determined whether its premises are true. Thus, to determine whether an argument is sound, you must come to know something about the way the actual world is.)

An argument is valid if and only if it is not possible for its premises to be true and its conclusion false at the same time.

True EXPLANATION: (That's correct: that's just the definition of "valid." Be sure to have this memorized!)

Any argument that is sound has true premises and a true conclusion.

True EXPLANATION: (That's right. An argument is sound iff (i) it is valid and (ii) it has true premises. We know that, if an argument is valid, then if it's premises are true, then its conclusion must also be true. So suppose we have a sound argument. Then we know, by (ii) in the definition of "sound," that its premises are true. And we know by the definition of "valid" that, if a valid argument has true premises, that its conclusion must also be true. Therefore, we know that, if an argument is sound, then its premises and conclusion must all be true.)

Every sound argument has true premises and a true conclusion.

True EXPLANATION: (That's right. An argument is sound iff (i) it is valid and (ii) it has true premises. We know that, if an argument is valid, then if it's premises are true, then its conclusion must also be true. So suppose we have a sound argument. Then we know, by (ii) in the definition of "sound," that its premises are true. And we know by the definition of "valid" that, if a valid argument has true premises, that its conclusion must also be true. Therefore, we know that, if an argument is sound, then its premises and conclusion must all be true.)

There are arguments that are valid, but unsound.

True EXPLANATION: (That's right. An argument might be valid, but it might nevertheless be unsound. This happens when it is not possible for the premises to be true and the conclusion false, but one or more of the premises is not true. For instance, the following argument is valid, but unsound: (P1) If Clinton is the President, then Kaine is Vice President. (P2) Clinton is the President. (C) Therefore, Kaine is Vice President. If the premises are true, then the conclusion must be true. Therefore, the argument is valid. However, the second premise is false: Clinton is not President. Since an argument is sound iff (i) it is valid and (ii) its premises are all true, the argument is unsound.)

Different assignments are due on different days of the week in this class.

True EXPLANATION: (That's right. In the past, I have required everything for the week due at 11:59PM on Sunday. In practice, this means that most students won't start doing the work until around 8PM Sunday night. This is bad because a few hours once a week isn't enough time to adequately work with the material.)

The following is valid: Columbus, Ohio is north of Cincinnati, Ohio. Cleveland, Ohio is north of Columbus, Ohio. Therefore, Cleveland is north of Cincinnati, Ohio.

True EXPLANATION: (That's right. It is not possible for the premises to be true and the conclusion false, given the meaning of the words in the argument.)

True/False: If a substitution instance of an argument has true premises and a false conclusion, then all arguments of the same form are invalid.

True EXPLANATION: (That's right. That's exactly the sort of substitution instance we're looking for when we employ the counterexample/countermodel method.)

True/False: The following is a valid argument. (P1) Either we will go to the mountains or we will go to the beach. (P2) We will not go to the mountains. (C) Therefore, we will go to the beach.

True EXPLANATION: (That's right. To solve this, you needed to imagine that the premises were true and then determined whether the conclusion has to be true, as well. Imagine, then, that the premises are true. This would require that the second part of (P1)--the second disjunct "we will go to the beach"--is true. Since that is the conclusion, if the premises are true, then the conclusion has to be true.)

True/False: The following argument is valid. (P1) All men are readers. (P2) All readers are educated. (C) Therefore, all men are educated.

True EXPLANATION: (This is valid. Suppose the premises are true. Then the conclusion must be true, as well.)

True/False: The following argument is valid. Since London is north of Paris and south of Edinburgh, it follows that Paris is south of Edinburgh.

True EXPLANATION: (Try drawing the information contained in the premises. Is the conclusion true? Here's the argument in premise-conclusion form: (P1) London is north of Paris. (P2) London is south of Edinburgh. (C) Therefore, it follows that Paris is souh of Edinburgh.)

Symbolize the following Either Pablo Picasso or Salvador Dali ignored perspective, but it is not the case that both of them did. a. ((P ∨ S) ∙ ~(P ∙ S)) b. ((P ∨ S) ∨ ~(P ∙ S))

a. ((P ∨ S) ∙ ~(P ∙ S))

How is the following correctly symbolized? Either it is snowing or it is raining. a. S ~ R b. S ∙ c. S ∨ R d. S ⊃ R

c. S ∨ R

Answer the following question using the definitions of 'valid' and 'sound': Suppose I know that an argument has true premises and a true conclusion. Can I conclude that the argument is sound? Why or why not?

written response (hw 3.A)

Answer the following question: If all we know about an argument is that it has true premises, we cannot conclude that it is valid or that it is sound. Why? In answering this, be sure to give the definitions of 'valid' and 'sound' and use these in constructing your answer.

written response (hw 3.A)

In the previous question, you specified the form of the following argument: Some fruits are green. Some fruits are apples. Therefore, some fruits are green apples. Now construct a countermodel to show that the argument is invalid.

written response (hw 4.A)

Using the letters F, G, and A, state the form of the following argument: Some fruits are green. Some fruits are apples. Therefore, some fruits are green apples.

written response (hw 4.A) Some F are G, Some F are A, Therefore, some F are GA.

Construct and explain a counterexample/countermodel to show that the following argument is invalid: Some numbers are odd. Some numbers are even. Therefore, some numbers are both odd and even. To do this, you will need to (i) identify the form of the argument and (ii) select values for the terms that show that the argument is invalid. Be sure to explain why your counterexample shows that the argument is invalid. (To do that, you'll need to appeal to the definition of "validity.)

written response (quiz 3)