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

Accepted Answer

The argument is valid because the conclusion $B \equiv F$ (B if and only if F) directly follows from the premise $B \cdot F$ (B and F) in all cases where the premise is true. A truth table would show that whenever $B \cdot F$ is true, $B \equiv F$ is also true, meaning there is no set of truth values that makes the premise true and the conclusion false, which is the condition for invalidity.

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

Accepted Answer

C

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

Accepted Answer

The argument is valid because there is no row in the truth table where the premises are true and the conclusion is false. The argument structure is such that if $A$ is true, then $∼B$ (not B) must also be true for the conclusion to follow. However, since the premises include $A \cup B$ (A or B), and the conclusion is $∼B$, the only way the argument could be invalid is if both $A$ and $B$ were false, which is not an option given the structure of the argument. Therefore, the argument is valid under all possible truth values for $A$ and $B$.

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

Accepted Answer

The argument is valid because the conclusion $E \cdot C$ follows logically from the premise $C \cdot E$ in all possible truth assignments. The order of conjunction ($\cdot$) does not affect the truth value of the statements; thus, if $C \cdot E$ is true, then $E \cdot C$ is also true, and vice versa.

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

Accepted Answer

The argument is a modus ponens, which is a valid argument form. It states that if N implies A (N → A), and N is true, then A must also be true. None of the truth value assignments show the argument to be invalid because in every case where N is true, A is also true, which aligns with the argument's conclusion.

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? $\frac { Q } { P \supset Q }$

Accepted Answer

An argument is invalid if it's possible for the premises to be true while the conclusion is false. For the argument given, the premise is $Q$ and the conclusion is $P \supset Q$ (if $P$ then $Q$). The material conditional ($\supset$) is false only if the antecedent ($P$) is true and the consequent ($Q$) is false. However, there's no option where $Q$ is true and the conclusion $P \supset Q$ is false, making the argument valid in all given cases.

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

Accepted Answer

An argument is invalid if it's possible for the premises to be true while the conclusion is false. The given argument, from $B \cdot A$ to $A$, is valid because whenever $B \cdot A$ is true (meaning both $B$ and $A$ are true), $A$ is necessarily true. None of the provided truth value assignments show a case where the premise is true and the conclusion is false, thus 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? $\frac { N } { N \equiv T}$

Accepted Answer

The answer of Use a truth table to answer the...

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

Accepted Answer

An argument is invalid if it's possible for the premises to be true while the conclusion is false. The given argument has the premise $M \cdot U$ (M AND U) and the conclusion $M \vee U$ (M OR U). For any combination of truth values for M and U where the premise is true, the conclusion will also be true. This is because if both M and U are true (which they must be for the premise to be true), then at least one of them is true, making the conclusion true. Therefore, the argument is valid, and there is no set of truth values that makes the argument invalid.

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

Accepted Answer

The argument is a valid modus tollens form. If L implies E, and E is false, then L must also be false. None of the truth value assignments show the argument to be invalid.

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

Accepted Answer

The answer of Use a truth table to answer the...

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

Accepted Answer

The argument is valid because the premises logically lead to the conclusion. The first premise states that either B or T is true. The second premise negates B, leaving T as the only option, which matches the conclusion.

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

Accepted Answer

The argument is invalid if there is a case where the premises are true and the conclusion is false. In option C, O is false and Y is true, making the premise "O ⊃ Y" true (since a false antecedent makes the implication true), the second premise "Y" true, but the conclusion "O" false.

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

Accepted Answer

For the argument to be invalid, the premise must be true and the conclusion false. In option C, ~D is true (since D is false), and C ⊃ D is false (since C is true and D is false), making the argument invalid.

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

Accepted Answer

The argument is invalid if there is a case where the premises are true and the conclusion is false. In option D, R is false and T is false, making the premise R ≡ T true (since both are false), but the conclusion R is false.

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

Accepted Answer

The answer of Use a truth table to answer the...

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

Accepted Answer

The argument is valid because in every possible scenario where the premise $Z \equiv A$ is true, the conclusion $Z \supset A$ is also true. The biconditional $Z \equiv A$ means Z and A have the same truth value, and $Z \supset A$ means if Z is true, then A is also true, which is satisfied in all cases where $Z \equiv A$ holds.

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

Accepted Answer

An argument is invalid if it's possible for the premises to be true while the conclusion is false. In this case, the premise is $\sim M$ (not M), and the conclusion is $M \supset N$ (if M then N). For the argument to be invalid, we would need a situation where $\sim M$ is true, but $M \supset N$ is false. However, $M \supset N$ is only false when M is true and N is false. Since the premise $\sim M$ means M is false, there's no situation where the premise is true and the conclusion is false, making the argument 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? $$\begin{array} { l } 
E \supset S \
S \supset E \
E \equiv S
\end{array}$$

Accepted Answer

The argument is valid because all premises lead to the conclusion logically. In a valid argument, if the premises are true, the conclusion must also be true. The truth table for the given argument shows that for all possible truth values of E and S, the premises and the conclusion are consistent with each other. This means there is no set of truth values that would make the premises true and the conclusion false, which is the condition for an argument to be invalid.

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

Accepted Answer

An argument is invalid if it's possible for the premises to be true while the conclusion is false. In choice B, A is true, but $A \supset B$ (if A then B) is false because B is false, which directly shows the argument's invalidity under this truth assignment.

Quiz 10: Propositional Logic-Arguments

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

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

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

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

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

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? $\frac { Q } { P \supset Q }$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Quiz 10: Propositional Logic-Arguments

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? B⋅FB≡F\frac { B \cdot F } { B \equiv F }B≡FB⋅F​

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? A∪BA?B\begin{array} { l } A \cup B \\\frac { A } { ?B }\end{array}A∪B?BA​​

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⋅EE⋅C\frac { C \cdot E } { E \cdot C }E⋅CC⋅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? N⊃ANA\begin{array} { l } \mathrm { N } \supset \mathrm { A } \\\mathrm { N } \\\mathrm { A }\end{array}N⊃ANA​

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? QP⊃Q\frac { Q } { P \supset Q }P⊃QQ​

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? B⋅AA\frac { B \cdot A } { A }AB⋅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? NN≡T\frac { N } { N \equiv T}N≡TN​

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​

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

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? B∨T∼BT\begin{array} { l } \mathrm { B } \vee \mathrm { T } \\\sim \mathrm { B } \\\mathrm { T }\end{array}B∨T∼BT​

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? O⊃YYO\begin{array} { l } \mathrm { O } \supset \mathrm { Y } \\\mathrm { Y } \\\mathrm { O }\end{array}O⊃YYO​

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? ∼DC⊃D\frac { \sim \mathrm { D } } { \mathrm { C \supset } \mathrm { D }}C⊃D∼D​

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? R≡TR\frac { \mathrm { R } \equiv \mathrm { T } } { \mathrm { R } }RR≡T​

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? N∨C∼C∼N\begin{array} { l } \mathrm { N } \vee \mathrm { C } \\\sim \mathrm { C } \\\sim \mathrm { N }\end{array}N∨C∼C∼N​

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? Z≡AZ⊃A\frac { Z \equiv A } { Z \supset A }Z⊃AZ≡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? ∼MM⊃N\frac { \sim \mathrm { M } } { \mathrm { M \supset N }}M⊃N∼M​

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? E⊃SS⊃EE≡S\begin{array} { l } E \supset S \\S \supset E \\E \equiv S\end{array}E⊃SS⊃EE≡S​

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? AA⊃B\frac { A } { A\supset B}A⊃BA​

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

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

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

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

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? $\frac { Q } { P \supset Q }$

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

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

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

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

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

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

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

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

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

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

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

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

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