Deck 7: Deductive Reasoning: Propositional Logic

Question 1

The four logical connectives of propositional logic are conjunction,

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

Answer 1

disjunction, negation, and conditional.

Question 2

The symbolization for a conditional is

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

Answer 2

p $\rightarrow$ q.

Question 3

Propositional logic is the branch of deductive reasoning that deals with the logical relationships among

A) truth values.
B) arguments.
C) conditionals.
D) statements.

Answer 3

statements.

Question 4

A conditional is false only when the antecedent is _______ and the consequent is _______.

A) true; false
B) false; false
C) true; true
D) false; true

Question 5

The term _______ expresses logical conjunction.

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

Question 6

The terms either and neither usually signal the beginning of a

A) negation.
B) conditional.
C) conjunction.
D) disjunction.

Question 7

The first step in the short method is to

A) examine the conclusion.
B) locate the conditionals.
C) write out the symbolized argument in a single row.
D) find the conclusion of the argument.

Question 8

The procedure for confirming the validity of an argument by deducing its conclusion from its premises using simple, valid argument forms is known as the

A) short method.
B) method of proof.
C) technique of validity.
D) counterexample method.

Question 9

"It is not the case that the car is red and the truck is blue" can be symbolized by

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

Question 10

How is the argument form affirming the consequent symbolized?

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

Question 11

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

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

Question 12

The symbolization for a conjunction is

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

Question 13

In a disjunction, if one statement is false while the other is true, the whole disjunction is

A) false.
B) negated.
C) true.
D) both true and false.

Question 14

In propositional logic, the denial of a statement is called a

A) reductio ad absurdum.
B) negation.
C) refutation.
D) disjunction.

Question 15

What is the name of the following argument form?
P $\rightarrow$ q
Q $\rightarrow$ r
$\therefore$
p $\rightarrow$ r

A) Denying the consequent
B) Disjunctive syllogism
C) Modus tollens
D) Hypothetical syllogism

Question 16

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

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

Question 17

What is the name of the following rule of inference?
(p $\rightarrow$ q) & (r $\rightarrow$ s)
P v r
$\therefore$
q v s

A) Restrictive dilemma
B) Constructive dilemma
C) Disjunctive syllogism
D) Denying the consequent

Question 18

The idea behind _______ is that if the negation of a statement leads to falsehood, then the statement itself must be true.

A) denying the antecedent
B) modus tollens
C) reductio ad absurdum
D) modus ponens

Question 19

What is the name of the following rule of replacement?
~~p $\equiv$ p
P $\equiv$ ~~p

A) Simplification
B) Tautology
C) Modus tollens
D) Double negation

Question 20

The rules of replacement stipulate that some statements have the same

A) symbolic form.
B) truth value.
C) meaning.
D) logical connectives.

Question 21

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

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

Question 22

What is the symbolic form of the sentence "It is not the case that philosophy is dead, and it is not true that science has replaced it"?

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

Question 23

What symbolized argument does this truth table illustrate?
$$\begin{array} { l c c c } a & b & a \& b & a \\\hline T & T & T & T \\T & F & F & T \\F & T & F & F \\F & F & F & F\end{array}$$

A) a & b
$\therefore$
a
B) a & b ~a
$\therefore$
b
C) a & b
B & a
$\therefore$
a
D) ~a & b
$\therefore$
a

Question 24

Distribution and contraposition are names for two kinds of

A) logical connective.
B) compound statement.
C) rules of replacement.
D) rules of inference.

Question 25

The name of the following rule of replacement is
(p & q) $\equiv$ (q & p)
(p v q) $\equiv$ (q v p)

A) double negation.
B) association.
C) modus tollens.
D) commutation.

Question 26

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

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

Question 27

What is the symbolization for denying the antecedent?

A) p v q ~p
$\therefore$
q
B) P q
$\therefore$
p & q
C) p v q
Q $\rightarrow$ r
$\therefore$
p $\rightarrow$ r
D) p $\rightarrow$ q
~p
$\therefore$
~q

Question 28

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

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

Question 29

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

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

Question 30

What argument form does this truth table illustrate?
$$\begin{array} { c c c c c } x & y & z & x \rightarrow y & y \rightarrow z& x \rightarrow z \\\hline T & T & T & T & T &T\\T&T&F&T&F&F\\T&F&T&F&T&T \\T&F&F&F&T&T\\F&T&T&T&T&T\\F&T&F&T&F&T\\F&F&T&T&T&T\\F&F&F&T&T&T\end{array}$$

A) Affirming the consequent
B) Modus ponens
C) Hypothetical syllogism
D) Modus tollens

Question 31

The name of this rule of replacement-(p $\rightarrow$ q) $\equiv$ (~p v q)-is explication.

Question 32

A disjunction is an example of a compound statement.

Question 33

Each component statement in a compound statement is called a conjunct.

Question 34

If just one statement in a conjunction is false, the whole conjunction is false.

Question 35

If only one statement in a disjunction is true, the whole disjunction is false.

Question 36

If a negation is negated, the result is a positive statement.

Question 37

The truth table for a two-variable argument has eight rows.

Question 38

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

Question 39

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

Question 40

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

Question 41

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

Question 42

The sentence "Aaron and Robin are a team" is an example of a compound statement.

Question 43

"He supported the revolution, and he was arrested without being charged" is a conjunction.

Question 44

The symbolic form of modus tollens is
p v q
~p
$\therefore$ q

Question 45

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

Question 46

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

Question 47

The truth table for the following argument is:
$$\begin{array} { c c c c c } p & q & p \& q & p \rightarrow q & p \rightarrow ( p \& q ) \\\hline T & T & T & T & T \\T & F & F & F & F \\F & T & F & T & T \\F & F & F & T & T\end{array}$$

Question 48

The standard practice in propositional logic is to assume the exclusive sense of the word or when dealing with disjunctions.

Question 49

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

Question 50

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

Question 51

What are the four connectives in propositional logic, how are they symbolized, and what do they mean?

Question 52

How do parentheses change the meaning of symbolized statements?

Question 53

How are the six common argument forms highlighted in the text symbolized?

Question 54

What are the four steps of the short method?

Question 55

What are truth tables? How can truth tables be used to check the validity of arguments?

Question 56

What is the method of proof? When and how is it used?

Question 57

If an argument form is valid, what does that imply about other arguments using the same form? How does that fact help you evaluate arguments?

Question 58

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

Question 59

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

Question 60

Identify three of the most common rules of inference and give examples of how they are used.