Deck 10: Propositional Logic-Arguments

Question 1

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? $$\frac { B \cdot F } { B \equiv F }$$

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

Answer 1

None-the argument is valid.

Question 2

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? $$\begin{array} { l } \mathrm { T } \supset \mathrm { U } \\\sim \mathrm { T } \\\sim \mathrm { U }\end{array}$$

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.

Answer 2

T: F U: T

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? $\begin{array} { l } A \cup B \\\frac { A } { ?B }\end{array}$

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

Answer 3

None-the argument is valid.

Question 4

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? $$\frac { C \cdot E } { E \cdot C }$$

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

Question 5

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? $$\begin{array} { l } \mathrm { N } \supset \mathrm { A } \\\mathrm { N } \\\mathrm { A }\end{array}$$

A)N: T A: T
B)N: T A: F
C)N: F A: T
D)N: F A: 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? $\frac { Q } { P \supset Q }$

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

Question 7

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? $$\frac { B \cdot A } { A }$$

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

Question 8

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? $\frac { N } { N \equiv T}$

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

Question 9

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? $$\frac { M \cdot U } { M \vee U }$$

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 10

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? $$\begin{array} { l } \mathrm { L } \supset \mathrm { E } \\\sim \mathrm { E } \\\sim \mathrm { L }\end{array}$$

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 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? $\mathrm { G } \vee \mathrm { X }$
G
X

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

Question 12

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? $\begin{array} { l } \mathrm { B } \vee \mathrm { T } \\\sim \mathrm { B } \\\mathrm { T }\end{array}$

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

Question 13

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? $$\begin{array} { l } \mathrm { O } \supset \mathrm { Y } \\\mathrm { Y } \\\mathrm { O }\end{array}$$

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

Question 14

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? $\frac { \sim \mathrm { D } } { \mathrm { C \supset } \mathrm { D }}$

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

Question 15

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? $$\frac { \mathrm { R } \equiv \mathrm { T } } { \mathrm { R } }$$

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

Question 16

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? $\begin{array} { l } \mathrm { N } \vee \mathrm { C } \\\sim \mathrm { C } \\\sim \mathrm { N }\end{array}$

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

Question 17

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? $$\frac { Z \equiv A } { Z \supset A }$$

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

Question 18

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? $\frac { \sim \mathrm { M } } { \mathrm { M \supset N }}$

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

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? $$\begin{array} { l } E \supset S \\S \supset E \\E \equiv S\end{array}$$

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

Question 20

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? $\frac { A } { A\supset B}$

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

Question 21

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? $$\begin{array} { l } ( \mathrm { Z } \supset \mathrm { Y } ) \supset \mathrm { X } \\\mathrm { Z } \supset \mathrm {~W} \\\sim \mathrm { Y } \supset \sim \mathrm { W } \\\mathrm { V } \vee \mathrm { W }\end{array}$$

A)Z: T Y: T X: T W: T V: T
B)Z: T Y: T X: F W: F V: F
C)Z: F Y: F X: T W: F V: F
D)Z: F Y: F X: F W: F V: F
E)None-the argument is valid.

Question 22

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? $$\frac { [ ( C \cdot X ) \vee A ] \supset C } { C \supset [ ( X \vee A ) \supset C ] }$$

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

Question 23

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? $$\begin{array} { l } \mathrm { A } \supset ( \mathrm { J } \vee \mathrm { S } ) \\\sim \mathrm { J } \\\mathrm { S } \\\mathrm { A }\end{array}$$

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

Question 24

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? $$\begin{array} { l } \sim \mathrm { Z } \\\mathrm { C } \supset \mathrm { G } \\\mathrm { Z } \vee ( \mathrm { A } \supset \mathrm { C } ) \\\sim \mathrm { G } \supset \sim \mathrm { A }\end{array}$$

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

Question 25

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? $$\begin{array} { l } \mathrm { A } \equiv \mathrm { B } \\\mathrm { B } \equiv \mathrm { C } \\{ [ ( \mathrm { A } \cdot \mathrm { B } ) \cdot \mathrm { C } ] \cup [ ( \sim \mathrm { A } \cdot \sim \mathrm { B } ) \cdot \sim \mathrm { C } ] }\end{array}$$

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

Question 26

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? $$\begin{array} { l } ( \mathrm { S } \cdot \mathrm { D } ) \supset ( \mathrm { C } \cdot \mathrm { O } ) \\\mathrm { C } \supset \mathrm { D } \\\mathrm { S } \supset \mathrm { D }\end{array}$$

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

Question 27

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? $$\frac { \sim ( P \cdot I ) } { \sim P \vee \sim I }$$

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

Question 28

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? $$\begin{array} { l } \sim \mathrm { S } \supset ( \mathrm { L } \vee \mathrm { C } ) \\( \sim \mathrm { D } \cdot \sim \mathrm { C } ) \supset \mathrm { A } \\\sim \mathrm { L } \\\sim \mathrm { C } \supset ( \mathrm { S } \cdot \mathrm { A } )\end{array}$$

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

Question 29

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? $$\begin{array} { l } ( \mathrm { H } \bullet \sim A ) \supset \mathrm { I } \\\mathrm { I } \supset \mathrm { W } \\( \mathrm { H } \bullet \mathrm { A } ) \supset \sim \mathrm { W }\end{array}$$

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

Question 30

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? $$\begin{array} { l } ( \mathrm { J } \bullet \sim \mathrm { V } ) \supset ( \mathrm { R } \vee \mathrm { D } ) \\\sim \mathrm { R } \\\sim \mathrm { D } \\\sim ( \mathrm { J } \bullet \sim \mathrm { V } )\end{array}$$

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

Question 31

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? $$\begin{array} { l } ( \mathrm { J } \bullet \sim \mathrm { V } ) \supset ( \mathrm { R } \vee \mathrm { D } ) \\\sim \mathrm { R } \\\sim \mathrm { D } \\\sim \mathrm { J }\end{array}$$

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

Question 32

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? $$\begin{array} { l } ( \mathrm { E }\cdot \sim \mathrm { H } ) \supset \mathrm { G } \\\sim ( \mathrm { H } \vee \mathrm { G } ) \\\sim \mathrm { E }\end{array}$$

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

Question 33

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? $$\frac { ( C \cdot M ) \supset C } { C \supset ( M \supset C ) }$$

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 34

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? $$\begin{array} { l } \mathrm { M } \supset \sim \mathrm { I } \\\mathrm { I } \supset \sim \mathrm { M } \\\mathrm { E } \supset \sim \mathrm { M } \\\mathrm { H } \supset \mathrm { E } \\\mathrm { H } \supset \mathrm { I }\end{array}$$

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

Question 35

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? $$\begin{array} { l } ( \mathrm { J } \bullet \sim \mathrm { V } ) \supset ( \mathrm { R } \vee \mathrm { D } ) \\\sim \mathrm { R } \\\sim \mathrm { D } \\\sim \mathrm { V }\end{array}$$

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

Question 36

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? $$\begin{array} { l } S \supset R \\\sim \mathrm { D } \\\mathrm { S } \supset \mathrm { D } \\\sim \mathrm { S }\end{array}$$

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 37

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? $$\begin{array} { l } \mathrm { D } \supset \sim \mathrm { W } \\\mathrm { H } \supset \sim \mathrm { C } \\\sim \mathrm { C } \supset \sim \mathrm { D } \\\mathrm { H } \supset \mathrm {W}\end{array}$$

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 38

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? $$\begin{array} { l } ( \mathrm { Z } \supset \mathrm { Y } ) \supset \mathrm { X } \\\mathrm { Z } \supset \mathrm { W } \\\sim \mathrm { Y } \supset \sim \mathrm { W } \\\mathrm { V } \vee \mathrm { X }\end{array}$$

A)Z: T Y: T X: T W: T V: T
B)Z: T Y: T X: F W: F V: F
C)Z: F Y: F X: T W: F V: F
D)Z: F Y: F X: F W: F V: F
E)None-the argument is valid.

Question 39

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? $$\frac { \sim \mathrm { I } \cup \mathrm { E } } { \mathrm { I } \supset \mathrm { E } }$$

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

Question 40

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? $$\begin{array} { l } W \supset \sim B \\X \supset \sim B \\( W \cup X ) \supset \sim B\end{array}$$

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

Question 41

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

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

Question 42

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? $$\begin{array} { l } \mathrm { P } \supset \mathrm { W } \\( \sim \mathrm { D } \cdot \mathrm { R } ) \supset \mathrm { W } \\\mathrm { P } \supset \sim \mathrm { D } \\( \mathrm { P } \vee \mathrm { R } ) \supset W\end{array}$$

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

Question 43

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

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

Question 44

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? $$\begin{array} { l } ( \mathrm { B } \cdot \mathrm { C } ) \supset \mathrm { F } \\( \mathrm { F } \cdot \mathrm { E } ) \supset ( \mathrm { J } \cdot \mathrm { P } ) \\\mathrm { B } \supset \mathrm { P }\end{array}$$

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

Question 45

Which rule is used in the following inference? $$\begin{array} { l } A \supset B \\A \\B\end{array}$$

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

Question 46

Which rule is used in the following inference? $$\begin{array} { l } ( A \cdot B ) \supset ( C \supset D ) \\A \cdot B \\C \supset D \end{array}$$

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

Question 47

Which, if any, of the following proofs are correct demonstrations of the validity of this argument? $$\begin{array}{l}\frac { ( A \cdot \sim D ) \cdot ( C \vee D ) } { C }\\\text { Proof } 1\\\begin{array} { l l l } \text { (1) } ( A \cdot \sim D ) \cdot ( C \vee D ) & / C & \text { Premise/Condusion } \\\text { (2) } \mathrm { C } \vee \mathrm { D } & & 1 \operatorname { Simp } \\\text { (3) } \sim \mathrm { D } & & 1 \operatorname { Simp } \\\text { (4) C } & & 2,3 \mathrm { DS } \\\text { Proof } 2 & & \\\text { (1) } ( \mathrm { A } \cdot \sim \mathrm { D } ) \cdot ( \mathrm { C } \vee \mathrm { D } ) & / \mathrm { C } & \text { Premise/Condusion } \\\text { (2) } \mathrm { C } \vee \mathrm { D } & & 1 \mathrm { Simp } \\\text { (3) } \mathrm { A } \cdot \sim \mathrm { D } && 1 \mathrm { Simp } \\\text { (4) } \sim \mathrm { D } && 3 \mathrm { Simp } \\\text { (5) C } && 2,4 \mathrm { DS }\end{array}\end{array}$$

A)Proof 1
B)Proof 2
C)Proofs 1 and 2
D)Neither proof
E)Not enough information is provided because proofs are incomplete.

Question 48

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

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

Question 49

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? $$\begin{array} { l } ( \mathrm { W } \bullet \sim \mathrm { A } ) \supset \mathrm { I } \\( \mathrm { A } \bullet \sim \mathrm { W } ) \supset \mathrm { M } \\\mathrm { E } \supset ( \sim \mathrm { W } \vee \sim \mathrm { A } ) \\\mathrm { E } \\\underline{\mathrm { G } \supset \sim ( \mathrm { I } \vee \mathrm { M } )} \\\sim \mathrm { G }\end{array}$$

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 50

Which rule is used in the following inference? $$\begin{array} { l } \sim ( \mathrm { F } \cdot \mathrm { K } ) \supset ( \mathrm { F } \supset \mathrm { L } ) \\\sim ( \mathrm { F } \supset \mathrm { L } ) \\\sim ( \mathrm { F } \cdot \mathrm { K } )\end{array}$$

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

Question 51

Which rule is used in the following inference? $$\begin{array} { l } ( \mathrm { I } \cdot \mathrm { J } ) \supset ( \mathrm { K } \vee \mathrm { L } ) \\\mathrm { I } \cdot \mathrm { J } \\\mathrm { K } \vee \mathrm { L }\end{array}$$

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

Question 52

Which rule is used in the following inference? $$\begin{array} { l } \sim ( A \equiv B )\supset( A \cup C ) \\\sim ( A \cup C ) \\\sim ( A \equiv B )\end{array}$$

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

Question 53

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? $$\begin{array} { l } S \supset R \\\sim \mathrm { D } \\S\supset D \\\sim R\end{array}$$

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 54

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? $$\begin{array} { l } \mathrm { C } \supset ( \mathrm { P } \cdot \mathrm { B } ) \\( \mathrm { P } \supset \mathrm { E } ) \cdot ( \mathrm { B } \supset \mathrm { W } ) \\( \mathrm { W } \cdot \mathrm { E } ) \supset \sim \mathrm { T } \\\mathrm { T }\\\sim \mathrm {C } \end{array}$$

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

Question 55

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

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

Question 56

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

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

Question 57

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? $$\begin{array} { l } \mathrm { I } \supset \sim \mathrm { B } \\\sim \mathrm { I } \supset \sim \mathrm { P } \\\mathrm { G } \supset ( \mathrm { B } \cdot \mathrm { P } ) \\\sim \mathrm { G }\end{array}$$

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

Question 58

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? $$\begin{array} { l } ( \mathrm { B } \cdot \mathrm { C } ) \supset \mathrm { F } \\( \mathrm { F } \cdot \mathrm { E } ) \supset ( \mathrm { J } \cdot \mathrm { P } ) \\( \mathrm { B } \cdot \mathrm { C } ) \supset \mathrm { P }\end{array}$$

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

Question 59

Which rule is used in the following inference? $$\begin{array} { l } \mathrm { J } \supset \mathrm { R } \\\sim \mathrm { R } \\\sim \mathrm { J }\end{array}$$

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

Question 60

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

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

Question 61

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

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

Question 62

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

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

Question 63

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

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

Question 64

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form.

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

Question 65

Which rule is used in the following inference? $$\begin{array} { l } \mathrm { D } \vee \mathrm { L } \\\frac { \sim \mathrm { D } } { \mathrm { L } }\end{array}$$

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

Question 66

Which rule is used in the following inference? $$\begin{array} { l } \sim [ ( \mathrm { F } \vee \mathrm { G } ) \cdot \mathrm { H } ] \supset \sim ( \mathrm { I } \equiv \mathrm { J } ) \\\sim \sim ( \mathrm { I } \equiv \mathrm { J } ) \\\sim \sim [ \mathrm { F } \vee \mathrm { G } ) \cdot \mathrm { H } ]\end{array}$$

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

Question 67

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

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

Question 68

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

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

Question 69

Which rule is used in the following inference? $$\begin{array} { l } ( B \cdot C ) \vee D \\\sim \mathrm { D } \\B \cdot C\end{array}$$

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

Question 70

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } ( \mathrm { M } \supset \mathrm { P } ) \supset ( \mathrm { L } \vee \mathrm { S } ) \\( \mathrm { L } \vee \mathrm { S } ) \supset ( \mathrm { T } \equiv W ) \\( \mathrm { M } \supset \mathrm { P } ) \supset ( \mathrm { T } \equiv W )\end{array}$$

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

Question 71

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

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

Question 72

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

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

Question 73

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $( \mathrm { N } \cdot \mathrm { D } ) \supset \mathrm { M }$
$\mathrm { N } \cdot \mathrm { D }$
M

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

Question 74

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

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

Question 75

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } { [ ( \mathrm { Y } \cdot \mathrm { A } ) \vee \sim \mathrm { N } ] \supset ( \mathrm { C } \cdot \mathrm { T } ) } \\\underline{( \mathrm { C } \cdot \mathrm { T } ) \supset ( \mathrm { I } \vee \mathrm { N } )} \\{ [ ( \mathrm { Y } \cdot \mathrm { A } ) \vee \sim \mathrm { N } ] \supset ( \mathrm { I } \vee \mathrm { N } ) }\end{array}$$

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

Question 76

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

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

Question 77

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } ( U \cup W ) \supset S \\S \supset C \\( U \vee W ) \supset C\end{array}$$

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

Question 78

Which rule is used in the following inference? $$\begin{array} { l } { [ ( Z \supset Y ) \cup ( Z \supset Y ) ] \supset [ \sim ( \sim A \cdot Z ) \supset ( \mathrm { X } \equiv Y ) ] } \\( Z \supset Y ) \cup ( Z \supset Y ) \\\sim ( \sim A \cdot \sim ) \supset ( \mathrm { X } \equiv Y )\end{array}$$

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

Question 79

The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj.Identify the form. $$\begin{array} { l } \sim \sim \mathrm{K} \\( Z \vee X ) \supset \sim K \\\sim ( Z \cup X )\end{array}$$

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

Question 80

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

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