Question 1

Consider: "Legalizing gay marriage will ultimately prove beneficial for gay individuals." Choose the best symbolization of the statement.

Accepted Answer

A)  L 
B)   L $\rightarrow$ G 
C)  L & G 
D)  L v G 
E)  none of these symbolizations fit 
A)  L 
B)   L $\rightarrow$ G 
C)  L & G 
D)  L v G 
E)  none of these symbolizations fit B

Question 2

A statement that consists of two simple statements is compound.

Accepted Answer

A) True 
 B)False  True

Question 3

The only time a conjunction is true is when both of its conjuncts are true.

Accepted Answer

A) True 
 B)False  True

Question 4

It is always the case that, if it is possible for an argument's premises to be true while its conclusion is false, then that argument is invalid.

Accepted Answer

A) True 
 B)False

Question 5

The following is a simple statement: "Both Michael and Jerry play basketball."

Accepted Answer

A) True 
 B)False

Question 6

A disjunction is symbolized by

Accepted Answer

A)  v 
B)  * 
C)  ^ 
D)  ~ 
A)  v 
B)  * 
C)  ^ 
D)  ~

Question 7

If we can sell our old house then we will have enough money to buy a new one. We're rich so we do have enough money to buy a new one. So we'll be able to sell our old house.

Accepted Answer

A)  S $\rightarrow$ M, R $\rightarrow$ M,   S; this argument is valid 
B)  S $\rightarrow$ M, R$\rightarrow$ M,   S; this argument is invalid 
C)  S $\rightarrow$M, R & ( R $\rightarrow$ M),   S; this argument is valid 
D)  S $\rightarrow$ M, R & (R $\rightarrow$ M),   S; this argument is invalid 
E)  none of the above 
A)  S $\rightarrow$ M, R $\rightarrow$ M,   S; this argument is valid 
B)  S $\rightarrow$ M, R$\rightarrow$ M,   S; this argument is invalid 
C)  S $\rightarrow$M, R & ( R $\rightarrow$ M),   S; this argument is valid 
D)  S $\rightarrow$ M, R & (R $\rightarrow$ M),   S; this argument is invalid 
E)  none of the above

Question 8

"If abortion should be illegal, it is because a fetus should be legally considered a person. But if a fetus should be legally considered a person then there should be no exception for abortion in the case of rape. Of course, there should be an exception for cases of rape. Therefore, abortion should not be illegal."

Accepted Answer

A) A $\rightarrow$P, P $\rightarrow$ ~ E, E  ~ A; this argument is valid 
B)  A $\rightarrow$ P, P $\rightarrow$ ~ E, E,   ~ A; this argument is invalid 
C)  P $\rightarrow$A, ~E $\rightarrow$ P, E,  ~ A; this argument is valid 
D)  P $\rightarrow$ A, ~E $\rightarrow$ P, E,   ~ A; this argument is invalid 
E)  none of the above 
A) A $\rightarrow$P, P $\rightarrow$ ~ E, E  ~ A; this argument is valid 
B)  A $\rightarrow$ P, P $\rightarrow$ ~ E, E,   ~ A; this argument is invalid 
C)  P $\rightarrow$A, ~E $\rightarrow$ P, E,  ~ A; this argument is valid 
D)  P $\rightarrow$ A, ~E $\rightarrow$ P, E,   ~ A; this argument is invalid 
E)  none of the above

Question 9

The physical laws of the universe are set up in such a way that they guarantee the formation of life the revolution. If God were to design the universe that's exactly how he would set it up. If God designed the universe then he exists. Therefore, God exists.

Accepted Answer

A)  L, D $\rightarrow$ L, D$\rightarrow$ E,   E; this argument is valid 
B)  L, D $\rightarrow$ L, D $\rightarrow$ E,   E; this argument is invalid 
C)  L, L $\rightarrow$ D, D $\rightarrow$ E,   E; this argument is valid 
D)  L, L $\rightarrow$D, D $\rightarrow$ E,   E; this argument is invalid 
E)  none of the above 
A)  L, D $\rightarrow$ L, D$\rightarrow$ E,   E; this argument is valid 
B)  L, D $\rightarrow$ L, D $\rightarrow$ E,   E; this argument is invalid 
C)  L, L $\rightarrow$ D, D $\rightarrow$ E,   E; this argument is valid 
D)  L, L $\rightarrow$D, D $\rightarrow$ E,   E; this argument is invalid 
E)  none of the above

Question 10

A conditional statement is symbolized by

Accepted Answer

A)  v 
B)  =) 
C)    
D)  $\rightarrow$ 
A)  v 
B)  =) 
C)    
D)  $\rightarrow$

Question 11

If the dog is sleeping you don't want to wake him up. The dog will start barking if you wake him. So, if the dog isn't sleeping then he is barking.

Accepted Answer

A)  S $\rightarrow$ ~ W, B $\rightarrow$ W,   ~ S $\rightarrow$ B; this argument is valid 
B)  S $\rightarrow$ ~ W, B $\rightarrow$ W,   ~ S $\rightarrow$ B; this argument is invalid 
C)  S $\rightarrow$ ~ W, W $\rightarrow$ B,   ~ S $\rightarrow$B; this argument is valid 
D)  S $\rightarrow$ ~ W, W $\rightarrow$  B,   ~ S $\rightarrow$ B; this argument is invalid 
E)  none of the above 
A)  S $\rightarrow$ ~ W, B $\rightarrow$ W,   ~ S $\rightarrow$ B; this argument is valid 
B)  S $\rightarrow$ ~ W, B $\rightarrow$ W,   ~ S $\rightarrow$ B; this argument is invalid 
C)  S $\rightarrow$ ~ W, W $\rightarrow$ B,   ~ S $\rightarrow$B; this argument is valid 
D)  S $\rightarrow$ ~ W, W $\rightarrow$  B,   ~ S $\rightarrow$ B; this argument is invalid 
E)  none of the above

Question 12

The statement "If Joan comes to the party, Harry won't come to the party" is correctly symbolized as

Accepted Answer

A)  p v ~q 
B)   p  ~q 
C)  J&~H 
D)  none of the above 
A)  p v ~q 
B)   p  ~q 
C)  J&~H 
D)  none of the above

Question 13

Consider: "If you can't fly then run, if you can't run then walk." Choose the best symbolization of the statement.

Accepted Answer

A)  (~F$\rightarrow$~R)$\rightarrow$~W 
B)  (~F$\rightarrow$~R)&(~R$\rightarrow$~W) 
C)  (~R$\rightarrow$~F)&(~W$\rightarrow$~R) 
D)  (~F$\rightarrow$R)$\rightarrow$~W 
E)  none of these symbolizations fit 
A)  (~F$\rightarrow$~R)$\rightarrow$~W 
B)  (~F$\rightarrow$~R)&(~R$\rightarrow$~W) 
C)  (~R$\rightarrow$~F)&(~W$\rightarrow$~R) 
D)  (~F$\rightarrow$R)$\rightarrow$~W 
E)  none of these symbolizations fit

Question 14

A truth table is a listing of all possible truth-values for the variables in an argument form.

Accepted Answer

A) True 
 B)False

Question 15

In the exclusive sense of the word "or," the phrase "A or B" means that either A is true or B is true but it is not the case that they are both true.

Accepted Answer

A) True 
 B)False

Question 16

Unless a speaker makes it abundantly clear, one should assume that the speaker is using the inclusive sense of the word "or."

Accepted Answer

A) True 
 B)False

Question 17

Had Hitler won World War II, he would've eventually had to deal with Japan. So, since if Hitler had had to deal with Japan millions more would've died, had Hitler won World War II millions more would've died.

Accepted Answer

A)  W $\rightarrow$D, D $\rightarrow$ M,   W $\rightarrow$ M; this argument is valid 
B)  W $\rightarrow$D, D $\rightarrow$ M,   W$\rightarrow$ M; this argument is invalid 
C)  D $\rightarrow$ W, M $\rightarrow$ W,   D $\rightarrow$ M; this argument is valid 
D)  D $\rightarrow$ W, M $\rightarrow$ W,  D $\rightarrow$ M; this argument is invalid 
E)  none of the above 
A)  W $\rightarrow$D, D $\rightarrow$ M,   W $\rightarrow$ M; this argument is valid 
B)  W $\rightarrow$D, D $\rightarrow$ M,   W$\rightarrow$ M; this argument is invalid 
C)  D $\rightarrow$ W, M $\rightarrow$ W,   D $\rightarrow$ M; this argument is valid 
D)  D $\rightarrow$ W, M $\rightarrow$ W,  D $\rightarrow$ M; this argument is invalid 
E)  none of the above

Question 18

The only time a conditional statement is false is when the antecedent is true and the conclusion is false.

Accepted Answer

A) True 
 B)False

Question 19

Either legalizing gay marriage will be beneficial for society or it will tear society apart. Legalizing mixed race marriage did not tear society apart and if so, legalizing gay marriage won't tear society apart. So, legalizing gay marriage will benefit society.

Accepted Answer

A)  B v T, M & (M$\rightarrow$ ~ T),  B; this argument is valid 
B)  B v T, M & (M $\rightarrow$ ~ T),  B; this argument is invalid 
C)  B v T, M $\rightarrow$ ~ T,   B; this argument is valid 
D)  B v T, M $\rightarrow$ ~ T,   B; this argument is invalid 
E)  none of the above 
A)  B v T, M & (M$\rightarrow$ ~ T),  B; this argument is valid 
B)  B v T, M & (M $\rightarrow$ ~ T),  B; this argument is invalid 
C)  B v T, M $\rightarrow$ ~ T,   B; this argument is valid 
D)  B v T, M $\rightarrow$ ~ T,   B; this argument is invalid 
E)  none of the above

Consider: "Legalizing gay marriage will ultimately prove beneficial for gay individuals." Choose the best symbolization of the statement.

A statement that consists of two simple statements is compound.

The only time a conjunction is true is when both of its conjuncts are true.

It is always the case that, if it is possible for an argument's premises to be true while its conclusion is false, then that argument is invalid.

The following is a simple statement: "Both Michael and Jerry play basketball."

A disjunction is symbolized by

If we can sell our old house then we will have enough money to buy a new one. We're rich so we do have enough money to buy a new one. So we'll be able to sell our old house.

The physical laws of the universe are set up in such a way that they guarantee the formation of life the revolution. If God were to design the universe that's exactly how he would set it up. If God designed the universe then he exists. Therefore, God exists.

A conditional statement is symbolized by

If the dog is sleeping you don't want to wake him up. The dog will start barking if you wake him. So, if the dog isn't sleeping then he is barking.

The statement "If Joan comes to the party, Harry won't come to the party" is correctly symbolized as

Consider: "If you can't fly then run, if you can't run then walk." Choose the best symbolization of the statement.

A truth table is a listing of all possible truth-values for the variables in an argument form.

In the exclusive sense of the word "or," the phrase "A or B" means that either A is true or B is true but it is not the case that they are both true.

Unless a speaker makes it abundantly clear, one should assume that the speaker is using the inclusive sense of the word "or."

Had Hitler won World War II, he would've eventually had to deal with Japan. So, since if Hitler had had to deal with Japan millions more would've died, had Hitler won World War II millions more would've died.

The only time a conditional statement is false is when the antecedent is true and the conclusion is false.

Either legalizing gay marriage will be beneficial for society or it will tear society apart. Legalizing mixed race marriage did not tear society apart and if so, legalizing gay marriage won't tear society apart. So, legalizing gay marriage will benefit society.

Introduction to Critical Thinking

Recognizing Arguments

Basic Logical Concepts

Language

Logical Fallacies--1

Logical Fallacies--2

A Little Categorical Logic, Analyzing Arguments, Evaluating Arguments and Truth Claims

Inductive Reasoning

Finding, Evaluating and Using Sources

Writing Argumentative Essays and Thinking Critically About the Media

Science and Pseudoscience

Filters

Exam 8: A Little Propositional Logic

Consider: "Legalizing gay marriage will ultimately prove beneficial for gay individuals." Choose the best symbolization of the statement.

A statement that consists of two simple statements is compound.

The only time a conjunction is true is when both of its conjuncts are true.

It is always the case that, if it is possible for an argument's premises to be true while its conclusion is false, then that argument is invalid.

The following is a simple statement: "Both Michael and Jerry play basketball."

A disjunction is symbolized by

If we can sell our old house then we will have enough money to buy a new one. We're rich so we do have enough money to buy a new one. So we'll be able to sell our old house.

The physical laws of the universe are set up in such a way that they guarantee the formation of life the revolution. If God were to design the universe that's exactly how he would set it up. If God designed the universe then he exists. Therefore, God exists.

A conditional statement is symbolized by

If the dog is sleeping you don't want to wake him up. The dog will start barking if you wake him. So, if the dog isn't sleeping then he is barking.

The statement "If Joan comes to the party, Harry won't come to the party" is correctly symbolized as

Consider: "If you can't fly then run, if you can't run then walk." Choose the best symbolization of the statement.

A truth table is a listing of all possible truth-values for the variables in an argument form.

In the exclusive sense of the word "or," the phrase "A or B" means that either A is true or B is true but it is not the case that they are both true.

Unless a speaker makes it abundantly clear, one should assume that the speaker is using the inclusive sense of the word "or."

Had Hitler won World War II, he would've eventually had to deal with Japan. So, since if Hitler had had to deal with Japan millions more would've died, had Hitler won World War II millions more would've died.

The only time a conditional statement is false is when the antecedent is true and the conclusion is false.

Either legalizing gay marriage will be beneficial for society or it will tear society apart. Legalizing mixed race marriage did not tear society apart and if so, legalizing gay marriage won't tear society apart. So, legalizing gay marriage will benefit society.

Introduction to Critical Thinking

Recognizing Arguments

Basic Logical Concepts

Language

Logical Fallacies--1

Logical Fallacies--2

A Little Categorical Logic, Analyzing Arguments, Evaluating Arguments and Truth Claims

Inductive Reasoning

Finding, Evaluating and Using Sources

Writing Argumentative Essays and Thinking Critically About the Media

Science and Pseudoscience

Filters