Question 1

For complex arguments, the truth-table method should be used to check for validity.

Accepted Answer

A) True 
 B)False  False

Question 2

What are rules of replacement? How and why are they used?

Accepted Answer

Rules of replacement are a set of logical equivalences that allow us to replace one statement with another statement that is logically equivalent. These rules are used in formal logic to manipulate and simplify logical expressions.

The rules of replacement are used to transform logical statements in order to make them easier to work with or to prove certain logical relationships. They are also used to show that two statements are logically equivalent, meaning that they have the same truth value in all possible scenarios.

For example, one of the rules of replacement is the double negation rule, which states that a statement is logically equivalent to its double negation. This means that if we have a statement "p", we can replace it with "not not p" and vice versa. This rule can be used to simplify complex logical expressions and make them easier to work with.

Another example is the rule of implication, which states that "p implies q" is logically equivalent to "not p or q". This rule can be used to transform conditional statements into disjunctions, which can be easier to work with in certain logical proofs.

Overall, the rules of replacement are used to manipulate logical statements in order to simplify them, prove logical relationships, and make them easier to work with in formal logic. They are an essential tool for anyone working with formal logic and are used to make logical reasoning more precise and rigorous.

Question 3

This rule of replacement-[(p & q) $\rightarrow$ r)] $ \equiv$ [p $\rightarrow$(q $\rightarrow$ r)]-is called contraposition.

Accepted Answer

A) True 
 B)False  False

Question 4

The term _______ expresses logical conjunction.

Accepted Answer

A)  not 
B)  unless 
C)  but 
D)  or 
A)  not 
B)  unless 
C)  but 
D)  or

Question 5

The terms but, yet, nevertheless, while, also, and moreover express logical conjunction.

Accepted Answer

A) True 
 B)False

Question 6

The rules of propositional logic that stipulate that some statements are logically equivalent are known collectively as the

Accepted Answer

A)  rules of inference. 
B)  method of proof. 
C)  rules of replacement. 
D)  short method. 
A)  rules of inference. 
B)  method of proof. 
C)  rules of replacement. 
D)  short method.

Question 7

In the method of proof, the rules are not used jointly but are applied one at a time and once per line.

Accepted Answer

A) True 
 B)False

Question 8

A disjunction is an example of a compound statement.

Accepted Answer

A) True 
 B)False

Question 9

The symbolization for a conjunction is

Accepted Answer

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

Question 10

What is the difference between the inclusive and the exclusive interpretations of a disjunction?

Accepted Answer

In logic and everyday language, a disjun

Question 11

The following is an accurate truth table for a conditional:
 $$\begin{array} { l c c } 
p & q & p \rightarrow q \
\hline T & T & T \
T & F & F \
F & T & T \
F & F & T
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 12

A statement composed of at least two statements is called a _______ statement.

Accepted Answer

A)  compound 
B)  conjunctive 
C)  disjunctive 
D)  conditional 
A)  compound 
B)  conjunctive 
C)  disjunctive 
D)  conditional

Question 13

The four logical connectives of propositional logic are conjunction,

Accepted Answer

A)  conditional, compound, and disjunction. 
B)  statement, disjunct, and conditional. 
C)  disjunction, negation, and conditional. 
D)  disjunct, conditional, and negation. 
A)  conditional, compound, and disjunction. 
B)  statement, disjunct, and conditional. 
C)  disjunction, negation, and conditional. 
D)  disjunct, conditional, and negation.

Question 14

In a truth table for a two-variable argument, what are the truth values for the first guide column?

Accepted Answer

A)  T, T, F, F 
B)  F, F, T, T 
C)  T, F, T, F 
D)  T, F, F, F 
A)  T, T, F, F 
B)  F, F, T, T 
C)  T, F, T, F 
D)  T, F, F, F

Question 15

The following is an accurate truth table for a conjunction:
 $$\begin{array} { l c c } 
p & q & p \& q \
\hline T & T & T \
T & F & F \
F & T & F \
F & F & F
\end{array}$$

Accepted Answer

A) True 
 B)False

Question 16

The symbolic form of "Either disembodied spirits exist, or psychic hoaxes are rampant" is

Accepted Answer

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

Question 17

What argument form does this truth table illustrate?
$$\begin{array} { l c c c c } 
p & q & p \rightarrow q & \sim p & \sim q \
\hline T & T & T & F & F \
T & F & F & F & T \
F & T & T & T & F \
F & F & T & T & T
\end{array}$$

Accepted Answer

A)  Affirming the consequent 
B)  Modus ponens 
C)  Denying the antecedent 
D)  Modus tollens 
A)  Affirming the consequent 
B)  Modus ponens 
C)  Denying the antecedent 
D)  Modus tollens

Question 18

What argument form does this truth table illustrate?
$$\begin{array} { l c c c c } 
p & q & p \rightarrow q & p & q \
\hline T & T & T & T & T \
T & F & F & T & F \
F & T & T & F & T \
F & F & T & F & F
\end{array}$$

Accepted Answer

A)  Affirming the consequent 
B)  Modus ponens 
C)  Denying the antecedent 
D)  Modus tollens 
A)  Affirming the consequent 
B)  Modus ponens 
C)  Denying the antecedent 
D)  Modus tollens

Question 19

The symbolization for a conditional is

Accepted Answer

A)  p v q. 
B)  p $\rightarrow$ q. 
C)  p*q. 
D)  p & q. 
A)  p v q. 
B)  p $\rightarrow$ q. 
C)  p*q. 
D)  p & q.

Question 20

The truth table for the following argument is:
 $$\begin{array} { l l c c c } 
a & b & a \& b & \sim a & b \
\hline T & T & T & F & T \
T & F & F & F & F \
F & T & F & T & T \
F & F & F & T & F
\end{array}$$

Accepted Answer

A) True 
 B)False

For complex arguments, the truth-table method should be used to check for validity.

What are rules of replacement? How and why are they used?

This rule of replacement-[(p & q) $\rightarrow$ r)] $\equiv$ [p $\rightarrow$ (q $\rightarrow$ r)]-is called contraposition.

The term _______ expresses logical conjunction.

The terms but, yet, nevertheless, while, also, and moreover express logical conjunction.

The rules of propositional logic that stipulate that some statements are logically equivalent are known collectively as the

In the method of proof, the rules are not used jointly but are applied one at a time and once per line.

A disjunction is an example of a compound statement.

The symbolization for a conjunction is

What is the difference between the inclusive and the exclusive interpretations of a disjunction?

The following is an accurate truth table for a conditional: p q p\rightarrowq T T T T F F F T T F F T

A statement composed of at least two statements is called a _______ statement.

The four logical connectives of propositional logic are conjunction,

In a truth table for a two-variable argument, what are the truth values for the first guide column?

The following is an accurate truth table for a conjunction: p q p\&q T T T T F F F T F F F F

The symbolic form of "Either disembodied spirits exist, or psychic hoaxes are rampant" is

What argument form does this truth table illustrate? p q p\rightarrowq \simp \simq T T T F F T F F F T F T T T F F F T T T

What argument form does this truth table illustrate? p q p\rightarrowq p q T T T T T T F F T F F T T F T F F T F F

The symbolization for a conditional is

The truth table for the following argument is: a b a\&b \sima b T T T F T T F F F F F T F T T F F F T F

The Power of Critical Thinking

Obstacles to Critical Thinking

Making Sense of Arguments

Reasons for Belief and Doubt

Media Manipulation: Fake News, Bias, and Advertising

Fallacies and Persuaders

Deductive Reasoning: Categorical Logic

Inductive Reasoning

Inference to the Best Explanation

Judging Scientific Theories

Critical Thinking in Morality and the Law

Filters

Exam 7: Deductive Reasoning: Propositional Logic

For complex arguments, the truth-table method should be used to check for validity.

What are rules of replacement? How and why are they used?

This rule of replacement-[(p & q) →\rightarrow→ r)] ≡ \equiv≡ [p →\rightarrow→ (q →\rightarrow→ r)]-is called contraposition.

The term _______ expresses logical conjunction.

The terms but, yet, nevertheless, while, also, and moreover express logical conjunction.

The rules of propositional logic that stipulate that some statements are logically equivalent are known collectively as the

In the method of proof, the rules are not used jointly but are applied one at a time and once per line.

A disjunction is an example of a compound statement.

The symbolization for a conjunction is

What is the difference between the inclusive and the exclusive interpretations of a disjunction?

The following is an accurate truth table for a conditional: p q p\rightarrowq T T T T F F F T T F F T

A statement composed of at least two statements is called a _______ statement.

The four logical connectives of propositional logic are conjunction,

In a truth table for a two-variable argument, what are the truth values for the first guide column?

The following is an accurate truth table for a conjunction: p q p\&q T T T T F F F T F F F F

The symbolic form of "Either disembodied spirits exist, or psychic hoaxes are rampant" is

What argument form does this truth table illustrate? p q p\rightarrowq \simp \simq T T T F F T F F F T F T T T F F F T T T

What argument form does this truth table illustrate? p q p\rightarrowq p q T T T T T T F F T F F T T F T F F T F F

The symbolization for a conditional is

The truth table for the following argument is: a b a\&b \sima b T T T F T T F F F F F T F T T F F F T F

The Power of Critical Thinking

Obstacles to Critical Thinking

Making Sense of Arguments

Reasons for Belief and Doubt

Media Manipulation: Fake News, Bias, and Advertising

Fallacies and Persuaders

Deductive Reasoning: Categorical Logic

Inductive Reasoning

Inference to the Best Explanation

Judging Scientific Theories

Critical Thinking in Morality and the Law

Filters

This rule of replacement-[(p & q) $\rightarrow$ r)] $\equiv$ [p $\rightarrow$ (q $\rightarrow$ r)]-is called contraposition.