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.

Accepted Answer

D

Question 2

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

Accepted Answer

The correct symbolization is "l $\rightarrow$ g" which translates to "If l (gay marriage is legalized), then g (gay individuals will be benefitted)." This is a direct representation of the conditional statement provided.

Question 3

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

Accepted Answer

The statement "If you can't fly, then run" is correctly symbolized as (~ f $\rightarrow$ r), where "~f" stands for "cannot fly" and "r" stands for "run". This is a direct translation of the given conditional statement into logical notation, indicating that if the condition of not being able to fly is true, then the action of running follows.

Question 4

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

Accepted Answer

The answer of Consider the statement "Terrorists hate our freedoms,...

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.

Accepted Answer

The answer of "Dogs make better pets because, although cats...

Question 6

A conditional statement is symbolized by _____.

Accepted Answer

The answer of A conditional statement is symbolized by _____.
...

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.

Accepted Answer

The answer of "If the dog is sleeping, you don't...

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."

Accepted Answer

The semicolon in the second statement does not change the meaning of the statement. Both statements are compound statements with two simple statements connected by the conjunction "and".

Question 9

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

Accepted Answer

The statement contains a grammatical error; it should be "Jerry plays basketball" instead of "Jerry play basketball."

Question 10

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

Accepted Answer

The statement is straightforward and describes a specific activity involving two individuals, making it simple.

Question 11

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

Accepted Answer

A truth table is a mathematical table used in logic to list all possible truth values of a logical expression based on its variables.

Question 12

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

Accepted Answer

Negation is indeed the grammatical operation whereby a proposition is replaced by one that states the opposite, often using "not" or equivalent words or phrases to express denial or contradiction.

Question 13

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

Accepted Answer

The answer of The statement "If Joan comes to the...

Question 14

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

Accepted Answer

A conditional statement is considered true if the antecedent (the "if" part) is false, regardless of the truth value of the consequent (the "then" part). This is because a conditional only promises that the consequent follows if the antecedent is true; it makes no promise about what happens when the antecedent is false.

Question 15

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

Accepted Answer

The statement is correctly symbolized as "~p & q" because it states that Frank (represented by p) is not a study animal, indicated by "~p", and Pete (represented by q) is a study animal, indicated by "q". The conjunction "&" combines these two conditions.

Question 16

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

Accepted Answer

The statement is correctly symbolized by ~(p & q) because it negates the conjunction of two propositions: Chicago losing (p) and Green Bay winning (q), indicating that it is not the case that both of these events will happen together.

Question 17

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

Accepted Answer

The negation of a true statement is always false, as negation means stating the opposite of the original statement.

Question 18

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

Accepted Answer

An argument is considered invalid if it is possible for all the premises to be true while the conclusion is false, as this indicates a failure in logical connection between premises and conclusion.

Question 19

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

Accepted Answer

The statement is a negation of a disjunction, meaning it is not true that either of the conditions (Cynthia is married or Paula is engaged) is true. This is best represented by negating the entire disjunction, hence ~(p & q), which correctly symbolizes the statement.

Question 20

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

Accepted Answer

The correct symbolization of the statement "Lucy is not a volleyball player, and Vesta is not a tennis player" is represented by "~ p & ~ q," where "~" stands for "not," "&" stands for "and," "p" could represent "Lucy is a volleyball player," and "q" could represent "Vesta is a tennis player." Thus, "~ p & ~ q" accurately captures the negation of both conditions.

Quiz 10: A Little Propositional Logic