Question 1

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } 
( \mathrm { N } \equiv \mathrm { C } ) \supset ( \mathrm { B } \vee \mathrm { F } ) \
( \mathrm { R } \cdot \mathrm { E } ) \supset ( \mathrm { N } \equiv \mathrm { C } ) \
( \mathrm { R } \cdot \mathrm { E } ) \supset ( \mathrm { B } \vee \mathrm { F } )
\end{array}$$

Accepted Answer

A) MP 
B) MT 
C) HS 
D) DS 
E) Conj

Question 2

The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD.Identify the form. $\frac { \underline { E } } { \mathrm{E} \vee[(\mathrm{R} \equiv \mathrm{F}) \cdot \mathrm{A}]}$

Accepted Answer

A) Simp 
B) Conj 
C) Add 
D) CD 
E) DD

Question 3

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $$\frac { ( C \cdot M ) \supset C } { C \supset ( M \supset C ) }$$

Accepted Answer

A) C: T M: T 
B) C: T M: F 
C) C: F M: T 
D) C: F M: F 
E) None-the argument is valid.

Question 4

Use a short form truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $$\begin{array} { l } 
S \supset R \
\sim \mathrm { D } \
\mathrm { S } \supset  \mathrm { D } \
\sim \mathrm { S }
\end{array}$$

Accepted Answer

A) S: T R: T D: T 
B) S: T R: T D: F 
C) S: F R: T D: F 
D) S: F R: F D: F 
E) None-the argument is valid.

Question 5

Use a short form truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $$\begin{array} { l } 
S \supset   R \
\sim \mathrm { D } \
S\supset   D \
\sim R
\end{array}$$

Accepted Answer

A) S: T R: T D: T 
B) S: T R: T D: F 
C) S: F R: T D: F 
D) S: F R: F D: F 
E) None-the argument is valid.

Question 6

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $$\begin{array} { l } 
\mathrm { T } \supset \mathrm { U } \
\sim \mathrm { T } \
\sim \mathrm { U }
\end{array}$$

Accepted Answer

A) T: T U: T 
B) T: T U: F 
C) T: F U: T 
D) T: F U: F 
E) None-the argument is valid.

Question 7

Use a short form truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $$\begin{array} { l } 
( \mathrm { W } \bullet \sim \mathrm { A } ) \supset \mathrm { I } \
( \mathrm { A } \bullet \sim \mathrm { W } ) \supset \mathrm { M } \
\mathrm { E } \supset ( \sim \mathrm { W } \vee \sim \mathrm { A } ) \
\mathrm { E } \
\underline{\mathrm { G } \supset \sim ( \mathrm { I } \vee \mathrm { M } )} \
\sim \mathrm { G }
\end{array}$$

Accepted Answer

A) W: T A: T I: T M: T E: T G: T 
B) W: T A: T I: T M: F E: T G: T 
C) W: F A: T I: T M: F E: T G: T 
D) W: F A: F I: F M: F E: T G: T 
E) None-the argument is valid.

Question 8

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } 
( \mathrm { Y } \cdot \mathrm { O } ) \supset \mathrm { R } \
\mathrm { R } \supset ( \mathrm { H } \cdot \mathrm { N } ) \
( \mathrm { Y } \cdot \mathrm { O } ) \supset ( \mathrm { H } \cdot \mathrm { N } )
\end{array}$$

Accepted Answer

A) MP 
B) MT 
C) HS 
D) DS 
E) Conj

Question 9

Which rule is used in the following inference? $\frac { \mathrm { K } \cdot \mathrm { G } } { \mathrm { G } }$

Accepted Answer

A) Simp 
B) Conj 
C) Add 
D) DS 
E) HS

Question 10

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } 
{ [ ( \mathrm { P } \equiv \mathrm { T } ) \cdot ( \mathrm { H } \cdot \mathrm { N } ) ] \supset ( \mathrm { T } \supset \sim \mathrm { S } ) } \
( \mathrm { T } \supset \sim \mathrm { S } ) \supset [ ( \mathrm { H } \vee \mathrm { E } ) \cup \mathrm { R } ] \
{ [ ( \mathrm { P } \equiv \mathrm { T } ) \cdot ( \mathrm { H } \cdot \mathrm { N } ) ] \supset [ ( \mathrm { H } \vee \mathrm { E } ) \vee \mathrm { R } ] }
\end{array}$$

Accepted Answer

A) MP 
B) MT 
C) HS 
D) DS 
E) Conj

Question 11

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $$\frac { M \cdot U } { M \vee U }$$

Accepted Answer

A) M: T U: T 
B) M: T U: F 
C) M: F U: T 
D) M: F U: F 
E) None-the argument is valid.

Question 12

Use a short form truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $$\begin{array} { l } 
\mathrm { D } \supset \sim \mathrm { W } \
\mathrm { H } \supset \sim \mathrm { C } \
\sim \mathrm { C } \supset \sim \mathrm { D } \
\mathrm { H } \supset  \mathrm {W}
\end{array}$$

Accepted Answer

A) D: T W: T H: T C: T 
B) D: T W: T H: F C: F 
C) D: F W: F H: T C: F 
D) D: F W: F H: F C: F 
E) None-the argument is valid.

Question 13

Which rule is used in the following inference? $$\sim A \supset R$$
$\sim R$
$\sim A$

Accepted Answer

A) HS 
B) MP 
C) MT 
D) CD 
E) DD

Question 14

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } 
( \mathrm { R } \supset \mathrm { R } ) \supset ( \mathrm { D } \equiv \sim \mathrm { U } ) \
\frac { \mathrm { R } \supset \mathrm { R } } { \mathrm { D } \equiv \sim \mathrm { U } }
\end{array}$$

Accepted Answer

A) MP 
B) MT 
C) HS 
D) DS 
E) Conj

Question 15

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } 
\mathrm { F } \supset \mathrm { F } \
\mathrm { F } \
\mathrm { F }
\end{array}$$

Accepted Answer

A) MP 
B) MT 
C) HS 
D) DS 
E) Conj

Question 16

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } 
( \mathrm { P } \cdot \mathrm { R } ) \supset A \
P \cdot R\
A
\end{array}$$

Accepted Answer

A) MP 
B) MT 
C) HS 
D) DS 
E) Conj

Question 17

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } 
{ [ ( \mathrm { G } \cdot \mathrm { R } ) \equiv ( \mathrm { S } \supset \mathrm { P } ) ] \supset ( \mathrm { N } \cdot \mathrm { G } ) } \
\sim ( \mathrm { N } \cdot \mathrm { G } ) \
\sim [ ( \mathrm { G } \cdot \mathrm { R } ) \equiv ( \mathrm { S } \supset \mathrm { P } ) ]
\end{array}$$

Accepted Answer

A) MP 
B) MT 
C) HS 
D) DS 
E) Conj

Question 18

Which rule is used in the following inference? $$\begin{array} { l } 
[ A \cdot ( B \cdot \mathrm { C } ) ] \supset ( \mathrm { B } \vee \mathrm { D } ) ] \
( \mathrm { B } \vee \mathrm { D } ) \supset [ \mathrm { E } \vee ( \mathrm { F } \cdot \mathrm { G } ) ] \
{ [ \mathrm { A } \cdot ( \mathrm { B } \cdot \mathrm { C } ) ] \supset [ \mathrm { E } \vee ( \mathrm { F } \cdot \mathrm { G } ) ] }
\end{array}$$

Accepted Answer

A) HS 
B) MP 
C) MT 
D) CD 
E) DD

Question 19

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $$\begin{array} { l } 
\mathrm { L } \supset \mathrm { E } \
\sim \mathrm { E } \
\sim \mathrm { L }
\end{array}$$

Accepted Answer

A) L: T E: T 
B) L: T E: F 
C) L: F E: T 
D) L: F E: F 
E) None-the argument is valid.

Question 20

Which rule is used in the following inference? $$\begin{array} { l } 
( \mathrm { D } \vee \sim \mathrm { E } ) \supset \mathrm { F } \
\mathrm { F } \supset ( \mathrm { G } \cdot \mathrm { H } ) \
( \mathrm { D } \vee \sim \mathrm { E } ) \supset ( \mathrm { G } \cdot \mathrm { H } )
\end{array}$$

Accepted Answer

A) HS 
B) MP 
C) MT 
D) CD 
E) DD

Exam 10: Propositional Logic-Arguments

The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD.Identify the form. $\frac { \underline { E } } { \mathrm{E} \vee[(\mathrm{R} \equiv \mathrm{F}) \cdot \mathrm{A}]}$

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $\frac { ( C \cdot M ) \supset C } { C \supset ( M \supset C ) }$

Use a short form truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $\begin{array} { l } S \supset R \\\sim \mathrm { D } \\\mathrm { S } \supset \mathrm { D } \\\sim \mathrm { S }\end{array}$

Use a short form truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $\begin{array} { l } S \supset R \\\sim \mathrm { D } \\S\supset D \\\sim R\end{array}$

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $\begin{array} { l } \mathrm { T } \supset \mathrm { U } \\\sim \mathrm { T } \\\sim \mathrm { U }\end{array}$

Which rule is used in the following inference? $\frac { \mathrm { K } \cdot \mathrm { G } } { \mathrm { G } }$

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $\frac { M \cdot U } { M \vee U }$

Which rule is used in the following inference? $\sim A \supset R$ $\sim R$ $\sim A$

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $\begin{array} { l } \mathrm { F } \supset \mathrm { F } \\\mathrm { F } \\\mathrm { F }\end{array}$

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $\begin{array} { l } ( \mathrm { P } \cdot \mathrm { R } ) \supset A \\P \cdot R\\A\end{array}$

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $\begin{array} { l } \mathrm { L } \supset \mathrm { E } \\\sim \mathrm { E } \\\sim \mathrm { L }\end{array}$

Which rule is used in the following inference? $\begin{array} { l } ( \mathrm { D } \vee \sim \mathrm { E } ) \supset \mathrm { F } \\\mathrm { F } \supset ( \mathrm { G } \cdot \mathrm { H } ) \\( \mathrm { D } \vee \sim \mathrm { E } ) \supset ( \mathrm { G } \cdot \mathrm { H } ) \end{array}$

Exam 10: Propositional Logic-Arguments

The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD.Identify the form. E‾E∨[(R≡F) ⋅A]\frac { \underline { E } } { \mathrm{E} \vee[(\mathrm{R} \equiv \mathrm{F}) \cdot \mathrm{A}]}E∨[(R≡F) ⋅A]E​​

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? (C⋅M) ⊃CC⊃(M⊃C) \frac { ( C \cdot M ) \supset C } { C \supset ( M \supset C ) }C⊃(M⊃C) (C⋅M) ⊃C​

Which rule is used in the following inference? K⋅GG\frac { \mathrm { K } \cdot \mathrm { G } } { \mathrm { G } }GK⋅G​

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? M⋅UM∨U\frac { M \cdot U } { M \vee U }M∨UM⋅U​

Which rule is used in the following inference? ∼A⊃R\sim A \supset R∼A⊃R ∼R\sim R∼R ∼A\sim A∼A

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. F⊃FFF\begin{array} { l } \mathrm { F } \supset \mathrm { F } \\\mathrm { F } \\\mathrm { F }\end{array}F⊃FFF​

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. (P⋅R) ⊃AP⋅RA\begin{array} { l } ( \mathrm { P } \cdot \mathrm { R } ) \supset A \\P \cdot R\\A\end{array}(P⋅R) ⊃AP⋅RA​

The following argument is an instance of one of the five inference forms Simp, Conj, Add, CD, DD.Identify the form. $\frac { \underline { E } } { \mathrm{E} \vee[(\mathrm{R} \equiv \mathrm{F}) \cdot \mathrm{A}]}$

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $\frac { ( C \cdot M ) \supset C } { C \supset ( M \supset C ) }$

Which rule is used in the following inference? $\frac { \mathrm { K } \cdot \mathrm { G } } { \mathrm { G } }$

Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? $\frac { M \cdot U } { M \vee U }$

Which rule is used in the following inference? $\sim A \supset R$ $\sim R$ $\sim A$

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $\begin{array} { l } \mathrm { F } \supset \mathrm { F } \\\mathrm { F } \\\mathrm { F }\end{array}$

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $\begin{array} { l } ( \mathrm { P } \cdot \mathrm { R } ) \supset A \\P \cdot R\\A\end{array}$