Deck 10: A Little Propositional Logic

Question 1

"I would make a New Year's resolution only if there was an objective measure of right and wrong. But there is no objective measure of right and wrong. Therefore, I wouldn't make a New Year's resolution." Choose the best symbolization of the statement and evaluate its validity.

A) o $\rightarrow$ r, ~ o, ~ r; this argument is invalid
B) r $\rightarrow$ o, ~ o, 11eea192_c70c_b5d8_aa9a_b73b90ea1ce6_TBMG1027_11 ~ r; this argument is invalid
C) None of the answers are correct
D) r $\rightarrow$ o, ~ o,11eea192_c70c_b5d8_aa9a_b73b90ea1ce6_TBMG1027_11 ~ r; this argument is valid
E) o $\rightarrow$ r, ~ o, 11eea192_c70c_b5d8_aa9a_b73b90ea1ce6_TBMG1027_11 ~ r; this argument is valid

Answer 1

r $\rightarrow$ o, ~ o, ~ r; this argument is valid

Question 2

Consider the statement "If gay marriage is legalized, then gay individuals will be benefitted." Choose the best symbolization of this statement.

A) None of the answers are correct
B) l
C) l $\rightarrow$ g
D) l v g
E) l & g

Answer 2

l $\rightarrow$ g

Question 3

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

A) (~ f $\rightarrow$ r)
B) (~ r $\rightarrow$ ~f )
C) None of the answers are correct
D) (~ f $\rightarrow$ ~ r)
E) (~ f $\rightarrow$ ~ r).

Answer 3

(~ f $\rightarrow$ r)

Question 4

Consider the statement "Terrorists hate our freedoms, yet the government has been removing those freedoms." Choose the best symbolization of this statement.

A) ( h & g) $\rightarrow$ r
B) None of the answers are correct
C) r $\rightarrow$ ( h & g)
D) h & r
E) h $\rightarrow$ r

Question 5

"Dogs make better pets because, although cats are cute, dogs are loyal. And if dogs are loyal they make better pets." Choose the best symbolization of the statement and evaluate its validity.

A) c & l, l $\rightarrow$ b, b; this argument is valid
B) c & l, l $\rightarrow$ b, 11eea193_1726_8a09_aa9a_c7212b6df936_TBMG1027_11 b; this argument is invalid
C) c & l, l & b, 11eea193_1726_8a09_aa9a_c7212b6df936_TBMG1027_11 b; this argument is invalid
D) c & l, l & b, 11eea193_1726_8a09_aa9a_c7212b6df936_TBMG1027_11 b; this argument is valid
E) None of the answers are correct

Question 6

A conditional statement is symbolized by _____.

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

Question 7

"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." Choose the best symbolization of the statement and evaluate its validity.

A) s $\rightarrow$ ~ w, w $\rightarrow$ b, ~ s $\rightarrow$ b; this argument is invalid
B) s $\rightarrow$ ~ w, b $\rightarrow$ w, 11eea193_6ab9_0a3b_aa9a_9515a3fcf1d3_TBMG1027_11 ~ s $\rightarrow$ b; this argument is valid
C) None of the answers are correct
D) s $\rightarrow$ ~ w, b $\rightarrow$ w, 11eea193_6ab9_0a3b_aa9a_9515a3fcf1d3_TBMG1027_11 ~ s $\rightarrow$ b; this argument is invalid
E) s $\rightarrow$ ~ w, w $\rightarrow$ b, 11eea193_6ab9_0a3b_aa9a_9515a3fcf1d3_TBMG1027_11 ~ s $\rightarrow$ b; this argument is valid

Question 8

There is no logical difference between the statements "Bob has an iPhone, and Ginny has a BlackBerry" and "Bob has an iPhone; however, Ginny has a BlackBerry."

Question 9

The following is a simple statement: "Michael plays football, and Jerry play basketball."

Question 10

The following is a simple statement: "Michael and Jerry are playing a game of basketball."

Question 11

A truth table is a list of all possible truth values.

Question 12

Negation is the use of the word "not," or an equivalent word or phrase, to deny a statement.

Question 13

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

A) j & ~ h
B) None of the answers are correct
C) p ~ q
D) p v ~ q

Question 14

If both the antecedent and consequent of a conditional are false, then that conditional is false.

Question 15

The statement "Frank isn't a study animal, but Pete is" is correctly symbolized as _____.

A) p & q
B) ~( p & q)
C) p v q
D) ~ p & q

Question 16

The statement "it is not the case that Chicago will lose and Green Bay will win" is correctly symbolized by ~( p & q).

Question 17

Sometimes, when a statement is true, its negation is also true.

Question 18

If there is any instance of all true premises followed by a false conclusion, the argument is invalid.

Question 19

The statement "It is not the case that Cynthia is married or Paula is engaged" is correctly symbolized as _____.

A) p & q
B) p v q
C) ~( p & q)
D) ~ p & q

Question 20

The statement "Lucy is not a volleyball player, and Vesta is not a tennis player" is correctly symbolized as _____.

A) ~ p v ~ q
B) l~v & v~t
C) ~( l & v)
D) ~ p & ~ q

Question 21

A disjunction is an "or" statement-that is, a statement that consists of two (or more) statements set apart, usually by the word "or."

Question 22

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

Question 23

"The air conditioner is on; however, the fan is not. So, it's cooler because if the air conditioner were on, it would be cooler." Choose the best symbolization of the statement and evaluate its validity.

A) a & ~ f, a $\rightarrow$ c, c; this argument is valid
B) a & ~ f, c, 11eea193_6ab9_0a3b_aa9a_9515a3fcf1d3_TBMG1027_11 a $\rightarrow$ c; this argument is invalid
C) None of the answers are correct
D) a & ~ f, a $\rightarrow$ c, 11eea193_6ab9_0a3b_aa9a_9515a3fcf1d3_TBMG1027_11 c; this argument is invalid
E) a & ~ f, c, 11eea193_6ab9_0a3b_aa9a_9515a3fcf1d3_TBMG1027_11 a $\rightarrow$ c; this argument is valid

Question 24

The word "or" is used in its nonexclusive sense in the statement "You can walk to the museum or you can take the bus."

Question 25

The statement "If Mark is a student, then he does not get paid" is correctly symbolized as _____.

A) p & ~ q
B) p $\rightarrow$ q
C) p $\rightarrow$ ~ q
D) p ~ q

Question 26

Consider the statement "Euthanasia could lead to a lack of compassion when dealing with the elderly, disabled, or the terminally ill." Choose the best symbolization of this statement.

A) None of the answers are correct
B) ( e & d) & t
C) ( e & d) v t
D) ( e v d) v t
E) e & ( d & t)

Question 27

Consider the statement "I don't know if I can tolerate that much tolerance." Choose the best symbolization of this statement.

A) t $\rightarrow$ ~k
B) ~k & ~t
C) None of the answers are correct
D) ~k $\rightarrow$ t
E) ~k

Question 28

"The physical laws of the universe are set up in such a way that they guarantee the formation of life. 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." Choose the best symbolization of the statement and evaluate its validity.

A) l, d $\rightarrow$ l, d $\rightarrow$ e, e; this argument is invalid
B) l, d $\rightarrow$ l, d $\rightarrow$ e, 11eea193_ef68_7a4d_aa9a_352430b8d78c_TBMG1027_11 e; this argument is valid
C) None of the answers are correct
D) l, l $\rightarrow$ d, d $\rightarrow$ e, 11eea193_ef68_7a4d_aa9a_352430b8d78c_TBMG1027_11 e; this argument is invalid
E) l, l $\rightarrow$ d, d $\rightarrow$ e, 11eea193_ef68_7a4d_aa9a_352430b8d78c_TBMG1027_11 e; this argument is valid

Question 29

"Had Hitler won World War II, he would have eventually had to deal with Japan. If Hitler had to deal with Japan, millions more would have died. Therefore, if Hitler had won World War II, millions more would have died." Choose the best symbolization of the statement and evaluate its validity.

A) None of the answers are correct
B) w $\rightarrow$ d, d $\rightarrow$ m, w $\rightarrow$ m; this argument is valid
C) d $\rightarrow$ w, m $\rightarrow$ w, 11eea193_ef68_7a4d_aa9a_352430b8d78c_TBMG1027_11d $\rightarrow$ m; this argument is invalid
D) w $\rightarrow$ d, d $\rightarrow$ m, 11eea193_ef68_7a4d_aa9a_352430b8d78c_TBMG1027_11 w $\rightarrow$ m; this argument is invalid
E) d $\rightarrow$ w, m $\rightarrow$ w, 11eea193_ef68_7a4d_aa9a_352430b8d78c_TBMG1027_11 d $\rightarrow$ m; this argument is valid

Question 30

"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." Choose the best symbolization of the statement and evaluate its validity.

A) a $\rightarrow$ p, p $\rightarrow$ ~ e, e, ~ a; this argument is valid
B) a $\rightarrow$ p, p $\rightarrow$ ~ e, e, 11eea19a_6932_3eff_aa9a_1566bd13e9ec_TBMG1027_11 ~ a; this argument is invalid
C) p $\rightarrow$ a, ~ e $\rightarrow$ p, e, 11eea19a_6932_3eff_aa9a_1566bd13e9ec_TBMG1027_11~ a; this argument is valid
D) None of the answers are correct
E) p $\rightarrow$ a, ~ e $\rightarrow$ p, e, 11eea19a_6932_3eff_aa9a_1566bd13e9ec_TBMG1027_11 ~ a; this argument is invalid

Question 31

A conjunction is true only when both of its statements are true.

Question 32

The statement "Lucky is brown, and Rover is black" is correctly symbolized as p & q.

Question 33

The statement "Vera is not a Republican, and Cal is not a Democrat" is correctly symbolized as ~( p & q).

Question 34

This argument follows the form known as modus tollens: "If the air conditioner is on, then it is hot outside. The air conditioner is on. Therefore, it is hot outside."

Question 35

The statement "Lara does not have a pen; however, Keith has one" is correctly symbolized as _____.

A) p v q
B) ~( p & q)
C) p & p
D) ~ p & q

Question 36

A statement might be true, or it might be false, or it might be neither true nor false.

Question 37

The symbol for the implication involved in an "if-then" statement is _____.

A) $\rightarrow$
B) ^
C) ~
D) *

Question 38

A compound statement consists of two or more statements, each of which can separately be considered either true or false.

Question 39

"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. Therefore, we'll be able to sell our old house." Choose the best symbolization of the statement and evaluate its validity.

A) s $\rightarrow$ m, r $\rightarrow$ m, s; this argument is invalid
B) s $\rightarrow$ m, r & ( r $\rightarrow$ m), 11eea19a_ca74_c671_aa9a_e7c69c0fc8ac_TBMG1027_11 s; this argument is valid
C) s $\rightarrow$ m, r $\rightarrow$ m, 11eea19a_ca74_c671_aa9a_e7c69c0fc8ac_TBMG1027_11 s; this argument is valid
D) None of the answers are correct
E) s $\rightarrow$ m, r & ( r $\rightarrow$ m), 11eea19a_ca74_c671_aa9a_e7c69c0fc8ac_TBMG1027_11 s; this argument is invalid

Question 40

"Either Oklahoma or Miami will win the game. Miami's going to win. Therefore, Oklahoma will lose." Choose the best symbolization of the statement and evaluate its validity.

A) ( o v m) & ~( o & m), m, ~ o; this argument is valid
B) o v m, m, 11eea19a_ca74_c671_aa9a_e7c69c0fc8ac_TBMG1027_11~ o; this argument is valid
C) o v m, m, 11eea19a_ca74_c671_aa9a_e7c69c0fc8ac_TBMG1027_11 ~ o; this argument is invalid
D) ( o v m) & ~(o & m), m, 11eea19a_ca74_c671_aa9a_e7c69c0fc8ac_TBMG1027_11 ~ o; this argument is invalid
E) None of the answers are correct

Question 41

In the context of propositional logic, which of the following statements is true?

A) The word ''and'' always joins two simple statements.
B) Every use of the word ''and'' indicates a compound statement that can be represented by p & q.
C) The words ''but'' and ''and'' cannot be used interchangeably.
D) Sometimes, ''and'' joins two things within the same simple statement.