Critical Thinking Midterm
In row 5 of your truth table, the truth values for the letters "p" and "q" are:
"p" is False and "q" is True.
In row 4 of your truth table, the truth values for the letters "p" and "q" are:
"p" is True and "q" is False.
Construct a truth table (using the method that is by now familiar to you) to determine whether the complex sentence below is a tautology, self-contradiction or a contingency. You will use this truth table to answer questions 19 - 20. Consider the complex sentence: p => ~p This sentence is:
A contingency.
Construct a truth table (using the method that is by now familiar to you) to determine whether the complex sentence-form below is a tautology, self-contradiction or a contingency. You will use this truth table to answer questions 4 - 7. Consider the complex sentence: (p => q) => (q => p). This sentence is:
A contingency.
Construct a truth table (using the method that is by now familiar to you) to determine whether the complex sentence below is a tautology, self-contradiction or a contingency. You will use this truth table to answer questions 15 - 18. Consider the complex sentence: (p => q) & ~(~p v q) This sentence is:
A self-contradiction.
Construct a truth table (using the method that is by now familiar to you) to determine whether the complex sentence below is a tautology, self-contradiction or a contingency. You will use this truth table to answer questions 12 - 14. Consider the complex sentence: ((p => q) & (q => r)) => ~(p & ~r) This sentence is:
A tautology .
Construct a truth table (using the method that is by now familiar to you) to determine whether the complex sentence below is a tautology, self-contradiction or a contingency. You will use this truth table to answer questions 8 - 11. Consider the complex sentence: q => (p v ~p). This sentence is:
A tautology .
"Your cellphone bill will be reasonable, provided that you use no more than 200 minutes each month. But you won't use more than 200 minutes in a month, so your bill will be reasonable."
Affirming the antecedent.
Consider the argument quoted in the paragraph below, and pick the argument form that best characterizes that argument. Be sure to convert all conditionals to standard form before you determine the form of the argument. (Also--you may find it helpful to assign letters to the individual statements in each argument, and to write out the form of the argument using those letters and the appropriate truth functional connectives before you answer). "If Joan is an actor, she'll have trouble finding work. Joan will have trouble finding work, so she is an actor."
Affirming the consequent.
In row 4 of your truth table, the truth values for the letters "p" and "q" are:
Both "p" and "q" are False.
In row 2 of your truth table, the truth values for premise (1) and (2) are:
Both premise (1) and premise (2) are False.
In row 6 of your truth table, the truth values for premise (1) and (2) are:
Both premise (1) and premise (2) are True.
In row 2 of your truth table, the truth values for premise (1) and the conclusion are:
Both premise (1) and the conclusion are False.
In row 4 of your truth table, the truth values for premise (1) and the conclusion are:
Both premise (1) and the conclusion are True.
Which of the following is a correct statement about row 2 of your truth table?
Both statement (1) and (2) are False
Which of the following is a correct statement about row 1 of your truth table?
Both statement (1) and statement (2) are True.
Which of the following is a correct statement about row 4 of your truth table?
Both statement (1) and statement (2) are True.
"If I go to bed at a decent hour tonight, I probably won't do very well on the exam tomorrow. But I won't do well on the exam if I stay up all night cramming, either. But since I either have to stay up cramming or go to bed at a decent hour, I guess I won't do well on the exam."
Constructive dilemma.
"If the team wins next week, they'll go to the bowl game. If the team ties next week, they'll win the conference championship. But the team will either win or tie, so they'll go to the bowl game or win the conference championship."
Constructive dilemma.
Nuclear power should be used because it is less damaging to the environment than fossil fuels. This sentence...
Contains an argument whose premise is 'nuclear power is less damaging to the environment than fossil fuels".
"If the TV is not plugged in, it won't work. But the TV is plugged in, so it will work."
Denying the antecedent.
"Without interesting work, life is tiresome. But life is not tiresome, so there is interesting work."
Denying the consequent.
"Terry has the choice of playing either kickball or soccer, but she won't play kickball, so she'll play soccer."
Disjunctive syllogism.
"There are two ways of carrying on a contest: one by law and the other by force. As the first one often fails, we must resort to the second."
Disjunctive syllogism.
The truth table for this argument has how many rows?
Eight (8)
A sound argument can have a false conclusion.
False
A sound argument can have a false premise.
False
A valid argument can have all true premises and a false conclusion.
False
Any argument (in English) contains at least one premise indicator word.
False
As long as the premises of an argument are connected to the conclusion it will be a good argument.
False
Examine the 'generic' truth table below. It contains truth values for two premises and the conclusion of an argument. Using the information contained in this table, answer the question below: Premise (1): Premise (2): Premise (3): 1). T T T 2). T F T 3). F T F 4). F F T 5). T T F 6). T F F 7). F F F 8). F T T Row two of this table proves that this argument is invalid.
False
In presenting an argument the conclusion is always given at the end.
False
On a separate piece of paper, construct a truth table to test the validity of the following argument: (1) (p v q) => (p & q) (2) ~(p v q) --------------------- p & q Be sure to construct the table just as you were instructed in the videos. You should have a column numbering the rows on the far left (number only the rows with T/F, not the 'header' row with the sentence letters and the statements); then columns for individual sentence-letters in alphabetical order, with truth values underneath them, then premise (1), then premise (2), then the conclusion. MAKE THE TRUTH TABLE NOW, and answer this question, and all questions through #11 using that truth table. This argument is valid.
False
On a separate piece of paper, construct a truth table to test the validity of the following argument: (1) p => q (2) p => (~r & q) --------------------- ~p Be sure to construct the table just as you were instructed in the videos. You should have a column numbering the rows on the far left (number only the rows with T/F, not the 'header' row with the sentence letters and the statements); then columns for individual sentence-letters in alphabetical order, with truth values underneath them, then premise (1), then premise (2), then the conclusion. MAKE THE TRUTH TABLE NOW, and answer this question, and all questions through #25 using that truth table. This argument is valid.
False
Row 2 of your truth table proves that this argument is invalid.
False
Row 4 of this table proves that this argument is invalid.
False
Row 4 of your truth table proves that this argument is invalid.
False
Row 7 of this truth table proves that this argument is invalid.
False
Suppose that the letters p, q, r, and s have the truth values stated in the chart below: p q r s T F T F What is the truth value of the expression below? (p v r) & (q v s)
False
Suppose that the letters p, q, r, and s have the truth values stated in the chart below: p q r s T F T F What is the truth value of the expression below? ~q => (p & s)
False
Suppose that the letters p, q, r, and s have the truth values stated in the chart below: p q r s T F T F What is the truth value of the expression below? s <=> (q => p)
False
Which phrase is a premise indicator?
For the reason that
The truth table for this argument has how many rows?
Four (4)
"If Roxanne knows that Cyrano speaks to her, she will fall in love with him. If she falls in love with Cyrano, Christian will be disappointed. So Christian will be disappointed if Roxanne knows that Cyrano is speaking."
Hypothetical syllogism.
"If global warming continues over the next 50 years, glaciers and polar ice caps will continue to melt. And Florida's coast will move inland by 1,000 feet, provided that glaciers and global ice caps continue to melt. So Florida's coast will move inland by 1,000 feet if global warming continues for the next 50 years."
Hypothetical syllogism.
(q & p) => r
If logic is fun and easy, then symbols can be used.
"q unless p."
If not-p, then q.
"p provided that q."
If q, then p.
"q is sufficient for p."
If q, then p.
Below is a sentence form in quotation marks. The "p" and "q" in the form stand for any grammatically correct sentence. Below the quoted form are five choices. Choose the letter next to the form that (1) means the same thing as the quoted sentence, AND (2) is in standard conditional form. "p if q."
If q, then p.
"Without checking your work, you won't find mistakes." Which sentence below (1) means the same thing as the sentence quoted above, AND (2) is in standard form?
If you do not check your work, then you will not find mistakes.
"You can play at Carnegie Hall only if you practice, practice practice." Which sentence below (1) means the same thing as the sentence quoted above, AND (2) is in standard form?
If you do not practice, practice, practice, then you cannot play at Carnegie Hall.
"You can learn to throw a frisbee if you really want to do it." Which sentence below (1) means the same thing as the sentence quoted above, AND (2) is in standard form?
If you really want to do it, then you can learn to throw a frisbee.
"Writing a thesis is a necessary condition for receiving a Master's Degree." Which sentence below (1) means the same thing as the sentence quoted above, AND (2) is in standard form?
If you received your Master's Degree, then you wrote a thesis.
"Returning your library books on time is a sufficient condition for avoiding library fines." Which sentence below (1) means the same thing as the sentence quoted above, AND (2) is in standard form?
If you return your library books on time, then you will avoid library fines.
"Whenever you want something very much, then you will work hard to achieve it." Which sentence below (1) means the same thing as the sentence quoted above, AND (2) is in standard form?
If you want something very much, then you will work hard to achieve it.
Roses are red. Sharks swim. ______________________ Detroit is in Michigan.
Is neither valid nor sound.
"As I see it, since you failed to provide the services specified this contract is null and void! For this reason, I don't owe you any more money." What is the function of the highlighted portion--"For this reason"--in this argument?
It is a conclusion indicator phrase
p & ~r
Logic is easy, but symbols cannot be used.
q & (~r => p)
Logic is fun, and if symbols cannot be used, then it is easy
~(q v p)
Logic is neither fun nor easy.
Suppose that an argument has a self-contradictory conclusion. Such an argument:
Might be valid or invalid--cannot tell from the information provided.
Suppose that an argument has all tautologous premises and a contingent conclusion. Such an argument:
Must be invalid
Suppose that an argument has a tautologous conclusion. Such an argument:
Must be valid
In row 1 of your truth table, the truth values for premise (1) and (2) are:
Premise (1) is True and premise (2) is False.
In the truth table you constructed for question #12, which choice below characterizes the truth values for the simple sentences "p" and "q" in row 6:
Sentence "p" is False, and sentence "q" is True.
In the truth table you constructed for question #8, which choice below characterizes the truth values for the simple sentences "p" and "q" in row 2:
Sentence "p" is True, and sentence "q" is False.
In the truth table you constructed for question #4, which choice below characterizes the truth values for the simple sentences "p" and "q" in row 3:
Sentence"p" is False, and sentence "q" is True.
Which of the following is a correct statement about row 3 of your truth table?
The "p" is False and the "q" is True.
In the truth table you constructed for question #15, which choice below characterizes the truth value for the complex sentence in row 1:
The complex sentence is False
In the truth table you constructed for question #15, which choice below characterizes the truth value for the complex sentence in row 4:
The complex sentence is False
In the truth table you constructed for question #4, which choice below characterizes the truth value for the complex sentence in row 3:
The complex sentence is False
In the truth table you constructed for question #12, which choice below characterizes the truth value for the complex sentence in row 4:
The complex sentence is True
In the truth table you constructed for question #19, which choice below characterizes the truth value for the complex sentence in row 2:
The complex sentence is True
In the truth table you constructed for question #4, which choice below characterizes the truth value for the complex sentence in row 2:
The complex sentence is True
In the truth table you constructed for question #8, which choice below characterizes the truth value for the complex sentence in row 2:
The complex sentence is True
In the truth table you constructed for question #8, which choice below characterizes the truth value for the complex sentence in row 4:
The complex sentence is True
In the truth table you constructed for question #15, which choice below characterizes the truth values for the simple sentences "p" and "q" in row 7:
There is no row 7 in this truth table.
All whales are mammals. All mammals live in the ocean . __________________________________ All whales live in the ocean.
This argument is valid, but unsound.
Which of the following is a conclusion indicator word or phrase?
Thus
A valid argument can have a false premise.
True
A valid argument can have all false premises and a false conclusion.
True
A valid argument can have some true premises, some false premises and a false conclusion.
True
An argument can be poor even if it has a true conclusion.
True
Consider the following two statements: (1) p => q (2) ~ (p & ~q) Using EXACTLY THE SAME method we used in the videos, construct a truth table to show whether these two statements are logically equivalent or not. To remind you: You will determine the number of rows in the table by counting the variables in the statements and using the method we used in the videos. The left column of your table will number the rows, the next columns will list the individual statement variables in alphabetical order, and there will be subsequent columns for every letter and truth functional connective in statements (1) and (2). Below the variables, you will place the appropriate Ts and Fs as we discussed in the videos, and you will calculate the truth values of statements (1) and (2) as we did in the videos. Make this table right now. It will be the basis of the question below, and the next four questions. Statements (1) and (2) are logically equivalent. (T/F)
True
Grass is green. Snow is white. __________________ Grass is green. This argument is valid.
True
On a separate piece of paper, construct a truth table to test the validity of the following argument: (1) (p & q) => r --------------------- (~r & q) => ~p Be sure to construct the table just as you were instructed in the videos. You should have a column numbering the rows on the far left (number only the rows with T/F, not the 'header' row with the sentence letters and the statements); then columns for individual sentence-letters in alphabetical order, with truth values underneath them, then the premises in order, then the conclusion. MAKE THE TRUTH TABLE NOW, and answer this question, and all questions through #18 using that truth table. This argument is valid.
True
Row 2 of your truth table proves that this argument is invalid.
True
Row 4 of your truth table proves that this argument is invalid.
True
Row 5 of this truth table proves that this argument is invalid.
True
Suppose that the letters p, q, r, and s have the truth values stated in the chart below: p q r s T F T F What is the truth value of the expression below? r => (q => (p & s))
True
This question is based on exercise set 8.8. Suppose that the letters p, q, r, and s have the truth values stated in the chart below: p q r s T F T F What is the truth value of the expression below? (p & r) v (q & s)
True
In England under the blasphemy laws it is illegal to express disbelief in the Christian religion. It is also illegal to teach what Christ taught on the subject of non-resistance. Therefore, whoever wishes to avoid being a criminal must profess to agree with Christ's teachings but must avoid saying what that teaching was. This is an argument with conclusion
Whoever wishes to avoid being a criminal must profess to agree with Christ's teachings but must avoid saying what that teaching was.
Logic is fun, and it is easy if symbols can be used.
q & (r => p)
Below you will see an italicized sentence. You are asked to translate that sentence into symbolic notation, using the sentence variables immediately below, and the symbols for truth functional connectives you have learned about in the readings and videos. (Note: we will use "&" for "and."). Choose the answer that corectly renders the quoted sentence into logical notation. Pay attention to the 'nots,' and be sure that all of your conditionals are in standard form!! p = "Logic is easy." q = "Logic is fun." r = "Symbols can be used." Logic is fun, but symbols cannot be used.
q & ~r
Either symbols can be used, or logic is easy but not fun.
r v (p & ~q)
Logic is easy unless symbols can be used.
~r => p
Logic is fun only if symbols can be used.
~r => ~q
Logic is not fun if symbols cannot be used.
~r => ~q
