Question 1

How could you symbolize the statement, "I will love you unless you kiss me"?
A)$ L \vee K $
B)L ? K
C)$~L\vee K$
D)L ? K

Accepted Answer

A

Question 2

~(p · ~q) is the same as:
A)~p · q
B)~p · ~q
C)(~p · ~q)
D)p ? q

Accepted Answer

D

Question 3

What is the symbolic representation of modus tollens?
A)p ? q q ? p
B)p ? q p ? q
C)p ? q ~q ? ~p
D)p ? q, ~q, ? p

Accepted Answer

Modus tollens is symbolically represented as "p → q, ~q, therefore ~p." This means if "p implies q" is true and "q is not true" (~q), then "p is not true" (~p) must also be true.

Question 4

q and ~~q mean the same thing.What does this illustrate?
A)material equivalence
B)logical equivalence
C)repetition
D)double negation

Accepted Answer

Double negation is a logical principle stating that negating a negation of a proposition results in the original proposition itself.

Question 5

"I will either kill you, or I will love you." This statement might be symbolized as:
A)$K\vee L$
B)~K · L
C)~K ? L
D)K ? L

Accepted Answer

Option A, $K \vee L$, correctly symbolizes the statement "I will either kill you, or I will love you," as it represents the logical disjunction that either K (kill) or L (love) will happen.

Question 6

"p ? q is logically equivalent to $~p\vee q$." This statement is:
A)De Morgan's Theorem
B)the definition of material implication
C)a negation of the conjunction of two statements
D)an invalid argument

Accepted Answer

The statement "p ? q is logically equivalent to $~p\vee q$" is the definition of material implication, which expresses the way conditional statements (if p, then q) are represented in propositional logic.

Question 7

Let B symbolize the statement "All birds are beautiful." Then ~B must symbolize all of the following, except:
A)Some bird is not beautiful.
B)No birds are beautiful.
C)It is not the case that all birds are beautiful.
D)It is false that all birds are beautiful.

Accepted Answer

Option B, "No birds are beautiful," is a stronger statement than simply negating "All birds are beautiful." The negation of "All birds are beautiful" implies that there is at least one bird that is not beautiful, not that all birds lack beauty.

Question 8

"If you can't use a computer, you won't get a job.I can use a computer very well, so I'm going to get a good job!"
 What is the best symbolic representation of this argument?
A)p ? q ~p ? ~q
B)$~p\vee ~q$ p ? ~q
C)p ? q ~q ? ~p
D)~p ? ~q, p, ? ~q

Accepted Answer

The argument can be symbolically represented as "p → q, p, ∴ q." This means "If p (you can use a computer), then q (you will get a job). I can use a computer (p), therefore, I will get a job (q)." Option A correctly represents this logic.

Question 9

"If dogs can fly, then the Earth is a sponge." Is this statement true?
Why or why not?
A)This is a contingent statement since it may be either true or false.
B)This is false but we must check the world to discover this.
C)This is false as neither the consequent nor the antecedent is true.
D)This is a true statement because it is in the form of a material conditional and has a false antecedent.

Accepted Answer

This statement is an example of a material conditional in logic, where if the antecedent ("If dogs can fly") is false, the entire conditional statement is considered true regardless of the truth value of the consequent ("then the Earth is a sponge"). This is a fundamental principle in classical logic, not requiring the actual truth of the consequent or its relation to reality, but rather focusing on the logical structure.

Question 10

Let B mean "the bread rises" and Y abbreviate "the yeast is good." The he compound statement B ? Y correctly represents any of the following propositions, except:
A)That the yeast is good is a necessary condition for the bread to rise.
B)That the yeast is good is a sufficient condition for the bread to rise.
C)The bread rises only if the yeast is good.
D)If the bread rises, the yeast is good.

Accepted Answer

The correct logical representation for "the yeast is good is a sufficient condition for the bread to rise" would be Y → B, meaning if Y (the yeast is good), then B (the bread rises). This does not necessarily imply that the bread can only rise if the yeast is good, as there could be other factors that cause the bread to rise. Choices A, C, and D all suggest that the goodness of the yeast is necessary for the bread to rise, which aligns with the logical statement B → Y (if the bread rises, then the yeast is good), but choice B incorrectly suggests the reverse.

Question 11

The following two arguments share the same argument form: "If wishes were horses, beggars could ride; beggars cannot ride; so wishes are not horses." "If price fixing becomes a common practice, the consumer will lose choices and taxpayers will be burdened with debt.We do not want consumers to lose choices and be burdened with debt, so we know that we should not allow price fixing."

Accepted Answer

The argument form is "If P, then Q; not Q; therefore, not P."

Question 12

A truth table for an argument contains one row in which there are Ts under the
 premises and an F under the conclusion.This single row shows that the entire argu-
 ment is invalid.

Accepted Answer

A truth table showing a row with true premises and a false conclusion demonstrates a logical inconsistency, indicating the argument is invalid.

Question 13

Another term for material equivalence is material implication.

Accepted Answer

Material equivalence and material implication are two different logical concepts. Material equivalence refers to a relationship where two statements are true or false under the same conditions, while material implication is a logical operation where if the first statement (the antecedent) is true, then the second statement (the consequent) must also be true.

Question 14

If an argument form is expressed as a conditional (with the conclusion as the consequent and a conjunction of the premises as the antecedent), and it shows one row on its truth table where Ts appear under the premises but an F appears under the conclusion, it may still be valid

Accepted Answer

An argument form expressed this way is considered valid only if there is no possible situation (row in the truth table) where the premises are all true (T) and the conclusion is false (F). If such a row exists, the argument form is invalid.

Question 15

The principle of excluded middle asserts that no statement can be both true and
 false at the same time.

Accepted Answer

The principle of excluded middle states that for any proposition, either that proposition is true, or its negation is true; it does not directly address whether a statement can be both true and false at the same time, which is more closely related to the law of non-contradiction.

Question 16

Matching:
-Two statements are logically equivalent if their biconditional is a ________.
A)tautology
B)statement
C)Proposition

Accepted Answer

Two statements are logically equivalent if their biconditional is a tautology, meaning it is true in all possible interpretations.

Question 17

Matching:
-p ? q is ________ equivalent to ~pV q.
A)sufficiently
B)logically
C)empirically

Accepted Answer

The statement "p → q" is logically equivalent to "~p ∨ q" in propositional logic, meaning if p then q is the same as not p or q.

Question 18

The only way for a disjunction to be false is if both of the disjuncts are proven to be ________ simultaneously.
A)True
B)False
C)Invalid

Accepted Answer

In a disjunction (an "or" statement), the overall statement is false only if both parts of the disjunction are false. If at least one part is true, the disjunction is true.

Question 19

Matching:
-Any statement is a ________ instance of its own statement form.
A)substitution
B)logical
C)Sufficient

Accepted Answer

A statement is a substitution instance of its own statement form because it is an example of that form with specific values or variables substituted into it.

Question 20

Matching:
-A conjunction is true only when both of its conjuncts are ________
A)false
B)true
C)valid

Accepted Answer

In logic, a conjunction is a compound statement formed by combining two statements using the conjunction "and." The conjunction itself is true if and only if both of the statements (conjuncts) it combines are true.

Quiz 8: Propositional Logic I

How could you symbolize the statement, "I will love you unless you kiss me"?

~(p · ~q) is the same as:

What is the symbolic representation of modus tollens?

q and ~~q mean the same thing.What does this illustrate?

"I will either kill you, or I will love you." This statement might be symbolized as:

"p ? q is logically equivalent to $~p\vee q$ ." This statement is:

Let B symbolize the statement "All birds are beautiful." Then ~B must symbolize all of the following, except:

"If you can't use a computer, you won't get a job.I can use a computer very well, so I'm going to get a good job!" What is the best symbolic representation of this argument?

"If dogs can fly, then the Earth is a sponge." Is this statement true? Why or why not?

Let B mean "the bread rises" and Y abbreviate "the yeast is good." The he compound statement B ? Y correctly represents any of the following propositions, except:

A truth table for an argument contains one row in which there are Ts under the premises and an F under the conclusion.This single row shows that the entire argu- ment is invalid.

Another term for material equivalence is material implication.

If an argument form is expressed as a conditional (with the conclusion as the consequent and a conjunction of the premises as the antecedent), and it shows one row on its truth table where Ts appear under the premises but an F appears under the conclusion, it may still be valid

The principle of excluded middle asserts that no statement can be both true and false at the same time.

Matching: -Two statements are logically equivalent if their biconditional is a ________.

Matching: -p ? q is ________ equivalent to ~pV q.

The only way for a disjunction to be false is if both of the disjuncts are proven to be ________ simultaneously.

Matching: -Any statement is a ________ instance of its own statement form.

Matching: -A conjunction is true only when both of its conjuncts are ________

Quiz 8: Propositional Logic I

How could you symbolize the statement, "I will love you unless you kiss me"?

~(p · ~q) is the same as:

What is the symbolic representation of modus tollens?

q and ~~q mean the same thing.What does this illustrate?

"I will either kill you, or I will love you." This statement might be symbolized as:

"p ? q is logically equivalent to p∨q~p\vee q p∨q ." This statement is:

Let B symbolize the statement "All birds are beautiful." Then ~B must symbolize all of the following, except:

"If you can't use a computer, you won't get a job.I can use a computer very well, so I'm going to get a good job!" What is the best symbolic representation of this argument?

"If dogs can fly, then the Earth is a sponge." Is this statement true? Why or why not?

Let B mean "the bread rises" and Y abbreviate "the yeast is good." The he compound statement B ? Y correctly represents any of the following propositions, except:

A truth table for an argument contains one row in which there are Ts under the premises and an F under the conclusion.This single row shows that the entire argu- ment is invalid.

Another term for material equivalence is material implication.

If an argument form is expressed as a conditional (with the conclusion as the consequent and a conjunction of the premises as the antecedent), and it shows one row on its truth table where Ts appear under the premises but an F appears under the conclusion, it may still be valid

The principle of excluded middle asserts that no statement can be both true and false at the same time.

Matching: -Two statements are logically equivalent if their biconditional is a ________.

Matching: -p ? q is ________ equivalent to ~pV q.

The only way for a disjunction to be false is if both of the disjuncts are proven to be ________ simultaneously.

Matching: -Any statement is a ________ instance of its own statement form.

Matching: -A conjunction is true only when both of its conjuncts are ________

"p ? q is logically equivalent to $~p\vee q$ ." This statement is: