Question 1

The truth table below demonstrates that the argument "(q v r) and ~r, so therefore q" is ___________________. $\begin{array}{|c|c|c|c|c|c|}\hline q&r&(qvr)&-r&((qvr)\&-r)&(((qvr)\&-r)\rightarrow q)\
\hline T & T & T & F & F & T \
\hline T & F & T & T & T & T \
\hline F&T&F&F&F&T\
\hline F&F&T&T&F&T\
\hline
\end{array}$

Accepted Answer

A)  valid 
B)  not valid 
C)  contingent 
D)  inconsistent

Question 2

Which of the following is a grammatically correct formula of declarative logic?

Accepted Answer

A)  (r v (~p & q) 
B)  (A & 
B)  
C)  ~(~p) 
D)  (((r & s) = s) v s) 
E)  ((~p & q) v ~r)

Question 3

Consider this argument: "If we buy tickets online, then we save money. If we ask for the student discount, then we save money. We did not ask for the student discount, but we did buy tickets online. So we saved money." Using a truth table to evaluate that argument for validity will produce a final column that ___________________.

Accepted Answer

A)  has eight rows all of which are T 
B)  has eight rows some of which are T and some F 
C)  has four rows all of which are F 
D)  has four rows all of which are T 
E)  has two rows both of which are T

Question 4

An argument is valid at the level of the Logic of Statements if the conditional formed by the conjunction of its premises as the antecedent and the conclusion as its consequent is a tautology.

Accepted Answer

A) True 
 B)False

Question 5

Consider this argument: "If we bought the movie tickets online or asked for the student discount, we saved a dollar per ticket. We did save a dollar per ticket. So we must have bought the tickets online or asked for the student discount." Using a truth table to evaluate that argument for validity will produce a final column that ___________________.

Accepted Answer

A)  has eight rows all of which are T 
B)  has eight rows some of which are T and some F 
C)  has four rows all of which are F 
D)  has four rows all of which are T 
E)  has two rows both of which are T

Question 6

A tautology is a grammatically correct expression that turns out to be true under every possible assignment of truth values to its component simple statements.

Accepted Answer

A) True 
 B)False

Question 7

Construct the truth table that defines negation.

Accepted Answer

The answer of Construct the truth table that defines negation....

Question 8

What is a simple declarative statement?

Accepted Answer

The answer of What is a simple declarative statement?...

Question 9

Statements A and B are __________________ in the Logic of Statements if, and only if, the bi-conditional (A ≡ B) is a tautology.

Accepted Answer

The answer of Statements A and B are __________________ in...

Question 10

Consider this argument: "If we bought the movie tickets online, we saved a dollar per ticket. We did buy the tickets online. So we must have saved a dollar per ticket." Using a truth table to evaluate that argument for validity will produce a final column that ___________________.

Accepted Answer

A)  has eight rows all of which are T 
B)  has eight rows some of which are T and some F 
C)  has four rows all of which are F 
D)  has four rows all of which are T 
E)  has two rows both of which are T

Question 11

________________ language is much richer than the notational language of the Logic of Declarative Statements. We can express only a limited range of the logical power of natural language using the tilde, ampersand, wedge, arrow, and triple bar.

Accepted Answer

The answer of ________________ language is much richer than the...

Question 12

Which of the following is the best translation of "If Lauren does not borrow my car, then she does not make it back to the campus on time for her Chemistry final and moreover she does not pass Chemistry."

Accepted Answer

A)  (p $\rightarrow$ q) 
B)  (p & q) 
C)  ((p $\rightarrow$ q) v ~q) 
D)  (~p $\rightarrow$ (~q & ~r)) 
E)  ((p v ~q) $\rightarrow$ r)

Question 13

Accurately and elegantly translate (~s → (~p & (~r & ~t))). Use these interpretations of the statement
letters:
p = "My son has chickenpox."
q = "I have to stay home from work."
r = "I need to take care of my son."
s = "My son is contagious."
t = "I need to call my boss."

Accepted Answer

The answer of Accurately and elegantly translate (~s → (~p...

Question 14

We can interpret the truth table below to be a demonstration that (q & p) and (p & q) are related to each other in what way(s)? $$\begin{array} { | c | c | c | c | c | } 
\hline p & q & ( p \& q ) & ( q \& p ) & ( p \& q ) = ( q \& p ) ) \
\hline T & T & T & T & T \
\hline T & F & F & F & T \
\hline F & T & F & F & T \
\hline F & F & F & F & T \
\hline
\end{array}$$

Accepted Answer

A)  They imply each other. 
B)  The second does not imply the first. 
C)  The first does not imply the second. 
D)  They are both tautologies. 
E)  They are both inconsistent.

Question 15

Which of the following is the best translation of "Lauren borrowed my car, although she could have taken her own."

Accepted Answer

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

Question 16

Compose a conjunction in English from these two simple statements: "We took Grandfather's advice." And "We had a great time." Let the first one be "p" and the second by "q" and translate the conjunction into symbolic logic.

Accepted Answer

The answer of Compose a conjunction in English from these...

Question 17

According to the following truth table, how should the formula ((p & q) $\rightarrow$ ~q) be characterized? $$\begin{array} { | c | c | c | c | c | } 
\hline p & q & ( p \& q ) & - q & ( p \& q ) \rightarrow - q ) \
\hline T & T & T & F & F \
\hline T & F & F & T & T \
\hline F & T & F & F & T \
\hline F & F & F & T & T \
\hline
\end{array}$$

Accepted Answer

A)  Contingent 
B)  Inconsistent 
C)  Disjunction 
D)  Tautology 
E)  Bi-Conditional

Question 18

Which of the following correctly describes a simple statement? "A grammatically correct construction in a given language used to assert ______________.

Accepted Answer

A)  that an idea is true 
B)  that a statement is false 
C)  that two statements are both true 
D)  that one or both of two statements are true 
E)  that if an antecedent statement is true, then a consequent statement is true

Question 19

Which of the following correctly describes a conditional statement? "A grammatically correct construction in a given language used to assert ______________.

Accepted Answer

A)  that an idea is true 
B)  that a statement is false 
C)  that two statements are both true 
D)  that one or both of two statements are true 
E)  that if an antecedent statement is true, then a consequent statement is true

Question 20

Construct the truth table that defines the conditional.

Accepted Answer

The answer of Construct the truth table that defines the...

Exam 17: The Logic of Declarative Statements

Which of the following is a grammatically correct formula of declarative logic?

An argument is valid at the level of the Logic of Statements if the conditional formed by the conjunction of its premises as the antecedent and the conclusion as its consequent is a tautology.

A tautology is a grammatically correct expression that turns out to be true under every possible assignment of truth values to its component simple statements.

Construct the truth table that defines negation.

What is a simple declarative statement?

Statements A and B are __________________ in the Logic of Statements if, and only if, the bi-conditional (A ≡ B) is a tautology.

Consider this argument: "If we bought the movie tickets online, we saved a dollar per ticket. We did buy the tickets online. So we must have saved a dollar per ticket." Using a truth table to evaluate that argument for validity will produce a final column that ___________________.

________________ language is much richer than the notational language of the Logic of Declarative Statements. We can express only a limited range of the logical power of natural language using the tilde, ampersand, wedge, arrow, and triple bar.

Which of the following is the best translation of "If Lauren does not borrow my car, then she does not make it back to the campus on time for her Chemistry final and moreover she does not pass Chemistry."

Accurately and elegantly translate (~s → (~p & (~r & ~t))). Use these interpretations of the statement letters: p = "My son has chickenpox." q = "I have to stay home from work." r = "I need to take care of my son." s = "My son is contagious." t = "I need to call my boss."

Which of the following is the best translation of "Lauren borrowed my car, although she could have taken her own."

Compose a conjunction in English from these two simple statements: "We took Grandfather's advice." And "We had a great time." Let the first one be "p" and the second by "q" and translate the conjunction into symbolic logic.

Which of the following correctly describes a simple statement? "A grammatically correct construction in a given language used to assert ______________.

Which of the following correctly describes a conditional statement? "A grammatically correct construction in a given language used to assert ______________.

Construct the truth table that defines the conditional.