Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: $\begin{array} {| l | } \hline \alpha\\\hline \text {1 }\\\hline \text {0 }\\\hline \end{array}$ For exercises with two propositional variables, the standard assignment is: \[\begin{array} { | c | c | } \hline \mathbf { n } & \boldsymbol { \beta } \\ \hline 1 & 1 \\ \hline 1 & 0 \\ \hline 0 & 1 \\ \hline 0 & 0 \\ \hline \end{array}\] For exercises with three propositional variables, the standard assignment is: \[\begin{array} { | c | c | c | } \hline \alpha & \beta & \gamma \\ \hline 1 & 1 & 1 \\ \hline 1 & 1 & 0 \\ \hline 1 & 0 & 1 \\ \hline 1 & 0 & 0 \\ \hline 0 & 1 & 1 \\ \hline 0 & 1 & 0 \\ \hline 0& 0 & 1 \\ \hline 0 & 0 &0\\ \hline \end{array}\] For exercises with four propositional variables, the standard assignment is: $\begin{array}{|c|c|c|c|} \hline\alpha & \beta & \gamma & \delta \\ \hline 1 & 1 & 1 & 1 \\ \hline 1 & 1 & 1 & 0 \\ \hline 1 & 1 & 0 & 1 \\ \hline 1 & 1 & 0 & 0\\ \hline 1 & 0 & 1 & 1 \\ \hline 1 & 0 & 1 & 0 \\ \hline 1 & 0 & 0 & 1 \\ \hline 1 & 0 & 0 & 0 \\ \hline 0 & 1 & 1 & 1 \\ \hline 0 & 1 & 1 & 0 \\ \hline 0 & 1 & 0 & 1\\ \hline 0 & 1 & 0 & 0 \\ \hline 0 & 0 & 1 & 1 \\ \hline 0 & 0 & 1 & 0 \\ \hline 0 & 0 & 0 & 1 \\ \hline 0 & 0 & 0 & 0\\\hline \end{array}$ Complete truth tables for each of the following propositions. -(D ≡ ∼D) ≡ (∼D ≡ D)

The answer of Note: the solutions to most of the...

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: $\begin{array} { |l| } \hline \alpha\\ \hline \text { 1}\\ \hline \text {0 }\\\hline \end{array}$ For exercises with two propositional variables, the standard assignment is: \[\begin{array} { | c | c | } \hline \alpha& \boldsymbol { \beta } \\ \hline 1 & 1 \\ \hline 1 & 0 \\ \hline 0 & 1 \\ \hline0& 0\\ \hline \end{array}\] For exercises with three propositional variables, the standard assignment is: \[\begin{array} { | c | c | c | } \hline \alpha & \beta & \gamma \\ \hline 1 & 1 & 1 \\ \hline 1 & 1 & 0 \\ \hline 1 & 0 & 1 \\ \hline 1 & 0& 0e \\ \hline 0 & 1 & 1 \\ \hline 0 & 1 & 0 \\ \hline 0 &0& 1 \\ \hline 0 & 0& 0 \\ \hline \end{array}\] For exercises with four propositional variables, the standard assignment is: \[\begin{array} { | l | l | l | l | } \hline \alpha & \boldsymbol { \beta } &\gamma& \delta\ \\ \hline 1 & 1 & 1 & 1 \\ \hline 1 & 1 & 1 & 0 \\ \hline 1 & 1 & 0 & 1 \\ \hline 1 & 1 & 0 & 0 \\ \hline 1 & 0 & 1 & 1 \\ \hline 1 & 0 & 1 & 0\\ \hline 1 & 0 & 0 & 1 \\ \hline 1 & 0& 0 & 0 \\ \hline 0 & 1 & 1 & 1 \\ \hline 0 & 1 & 1 &0 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | } \hline 0 & 1 & 0 & 1 \\ \hline 0 & 1 & 0 & 0 \\ \hline 0& 0 & 1 & 1 \\ \hline 0 & 0 & 1 & 0 \\ \hline 0 & 0 & 0 & 1 \\ \hline 0 & 0 & 0 & 0 \\ \hline \end{array}\] \[\begin{array} { |l | l | l | l |} \hline 0 & 1 & 0 & 1 \\ \hline \end{array}\] For each of the given propositions, determine which of the given sequences properly describes the column under the main operator, given the standard assignment of truth values to atomic propositions. -U ? (Z ? U)

A) 1100 B) 0011 C) 0001 D) 1110 A) 1100 B) 0011 C) 0001 D) 1110

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: $\begin{array} { |l| } \hline \alpha\\ \hline \text { 1}\\ \hline \text {0 }\\\hline \end{array}$ For exercises with two propositional variables, the standard assignment is: \[\begin{array} { | c | c | } \hline \alpha& \boldsymbol { \beta } \\ \hline 1 & 1 \\ \hline 1 & 0 \\ \hline 0 & 1 \\ \hline0& 0\\ \hline \end{array}\] For exercises with three propositional variables, the standard assignment is: \[\begin{array} { | c | c | c | } \hline \alpha & \beta & \gamma \\ \hline 1 & 1 & 1 \\ \hline 1 & 1 & 0 \\ \hline 1 & 0 & 1 \\ \hline 1 & 0& 0e \\ \hline 0 & 1 & 1 \\ \hline 0 & 1 & 0 \\ \hline 0 &0& 1 \\ \hline 0 & 0& 0 \\ \hline \end{array}\] For exercises with four propositional variables, the standard assignment is: \[\begin{array} { | l | l | l | l | } \hline \alpha & \boldsymbol { \beta } &\gamma& \delta\ \\ \hline 1 & 1 & 1 & 1 \\ \hline 1 & 1 & 1 & 0 \\ \hline 1 & 1 & 0 & 1 \\ \hline 1 & 1 & 0 & 0 \\ \hline 1 & 0 & 1 & 1 \\ \hline 1 & 0 & 1 & 0\\ \hline 1 & 0 & 0 & 1 \\ \hline 1 & 0& 0 & 0 \\ \hline 0 & 1 & 1 & 1 \\ \hline 0 & 1 & 1 &0 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | } \hline 0 & 1 & 0 & 1 \\ \hline 0 & 1 & 0 & 0 \\ \hline 0& 0 & 1 & 1 \\ \hline 0 & 0 & 1 & 0 \\ \hline 0 & 0 & 0 & 1 \\ \hline 0 & 0 & 0 & 0 \\ \hline \end{array}\] \[\begin{array} { |l | l | l | l |} \hline 0 & 1 & 0 & 1 \\ \hline \end{array}\] For each of the given propositions, determine which of the given sequences properly describes the column under the main operator, given the standard assignment of truth values to atomic propositions. -A ? [(?B $ \lor $ A) ? ?A]

A) 1100 B) 1001 C) 0011 D) 0001 E) 0000 A) 1100 B) 1001 C) 0011 D) 0001 E) 0000

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: $\begin{array} { |l| } \hline \alpha\\ \hline \text { 1}\\ \hline \text {0 }\\\hline \end{array}$ For exercises with two propositional variables, the standard assignment is: \[\begin{array} { | c | c | } \hline \alpha& \boldsymbol { \beta } \\ \hline 1 & 1 \\ \hline 1 & 0 \\ \hline 0 & 1 \\ \hline0& 0\\ \hline \end{array}\] For exercises with three propositional variables, the standard assignment is: \[\begin{array} { | c | c | c | } \hline \alpha & \beta & \gamma \\ \hline 1 & 1 & 1 \\ \hline 1 & 1 & 0 \\ \hline 1 & 0 & 1 \\ \hline 1 & 0& 0e \\ \hline 0 & 1 & 1 \\ \hline 0 & 1 & 0 \\ \hline 0 &0& 1 \\ \hline 0 & 0& 0 \\ \hline \end{array}\] For exercises with four propositional variables, the standard assignment is: \[\begin{array} { | l | l | l | l | } \hline \alpha & \boldsymbol { \beta } &\gamma& \delta\ \\ \hline 1 & 1 & 1 & 1 \\ \hline 1 & 1 & 1 & 0 \\ \hline 1 & 1 & 0 & 1 \\ \hline 1 & 1 & 0 & 0 \\ \hline 1 & 0 & 1 & 1 \\ \hline 1 & 0 & 1 & 0\\ \hline 1 & 0 & 0 & 1 \\ \hline 1 & 0& 0 & 0 \\ \hline 0 & 1 & 1 & 1 \\ \hline 0 & 1 & 1 &0 \\ \hline \end{array}\] \[\begin{array} { | c | c | c | c | } \hline 0 & 1 & 0 & 1 \\ \hline 0 & 1 & 0 & 0 \\ \hline 0& 0 & 1 & 1 \\ \hline 0 & 0 & 1 & 0 \\ \hline 0 & 0 & 0 & 1 \\ \hline 0 & 0 & 0 & 0 \\ \hline \end{array}\] \[\begin{array} { |l | l | l | l |} \hline 0 & 1 & 0 & 1 \\ \hline \end{array}\] For each of the given propositions, determine which of the given sequences properly describes the column under the main operator, given the standard assignment of truth values to atomic propositions. -(K ? L) ? (?K ? L)

A) 1111 B) 1010 C) 0110 D) 1000 E) 0001 A) 1111 B) 1010 C) 0110 D) 1000 E) 0001

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: $\begin{array} {| l | } \hline \alpha\\\hline \text {1 }\\\hline \text {0 }\\\hline \end{array}$ For exercises with two propositional variables, the standard assignment is: \[\begin{array} { | c | c | } \hline \mathbf { n } & \boldsymbol { \beta } \\ \hline 1 & 1 \\ \hline 1 & 0 \\ \hline 0 & 1 \\ \hline 0 & 0 \\ \hline \end{array}\] For exercises with three propositional variables, the standard assignment is: \[\begin{array} { | c | c | c | } \hline \alpha & \beta & \gamma \\ \hline 1 & 1 & 1 \\ \hline 1 & 1 & 0 \\ \hline 1 & 0 & 1 \\ \hline 1 & 0 & 0 \\ \hline 0 & 1 & 1 \\ \hline 0 & 1 & 0 \\ \hline 0& 0 & 1 \\ \hline 0 & 0 &0\\ \hline \end{array}\] For exercises with four propositional variables, the standard assignment is: $\begin{array}{|c|c|c|c|} \hline\alpha & \beta & \gamma & \delta \\ \hline 1 & 1 & 1 & 1 \\ \hline 1 & 1 & 1 & 0 \\ \hline 1 & 1 & 0 & 1 \\ \hline 1 & 1 & 0 & 0\\ \hline 1 & 0 & 1 & 1 \\ \hline 1 & 0 & 1 & 0 \\ \hline 1 & 0 & 0 & 1 \\ \hline 1 & 0 & 0 & 0 \\ \hline 0 & 1 & 1 & 1 \\ \hline 0 & 1 & 1 & 0 \\ \hline 0 & 1 & 0 & 1\\ \hline 0 & 1 & 0 & 0 \\ \hline 0 & 0 & 1 & 1 \\ \hline 0 & 0 & 1 & 0 \\ \hline 0 & 0 & 0 & 1 \\ \hline 0 & 0 & 0 & 0\\\hline \end{array}$ Complete truth tables for each of the following propositions. -[M $ \lor $ (N • O)] $ \lor $ [(M • N) $ \lor $ ∼(M • N)]

The answer of Note: the solutions to most of the...

Exam 2: Propositional Logic: Syntax and Semantic

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -A ⊃ B C ⊃∼B ∼A ⊃ D E ⊃∼F ∼E ⊃ G ∼F ⊃ C / D $\lor$ G

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Question 61

Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, specify a counterexample. -X / X $\lor$ [Y ≡ (Z • ∼X)]

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Question 62

construct a complete truth table for each of the following propositions. Then, using the truth table, classify each proposition as a tautology, a contingency, or a contradiction. Justify your answers by appeal to the meanings of those terms. -(I ⊃ ∼I) ⊃ [I ⊃ (I ⊃ ∼I)]

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Question 63

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P $\lor$ Q) ⊃ X] ≡ ∼(P $\lor$ Q)

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Question 64

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(∼P ⊃ P) $\lor$ (P ⊃ A)

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Question 65

For each of the following questions, determine whether the given formula is a wff or not. If it is a wff, indicate its main operator. -{∼R ⊃ [(Q • P) ⊃ S]}

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Question 66

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: \alpha 1 0 For exercises with two propositional variables, the standard assignment is: 1 1 1 0 0 1 0 0 For exercises with three propositional variables, the standard assignment is: \alpha \beta \gamma 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 For exercises with four propositional variables, the standard assignment is: \alpha \beta \gamma \delta 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 Complete truth tables for each of the following propositions. -(?C ? ?D) ? [D ? (C ? D)]

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Question 67

construct a complete truth table for each of the following propositions. Then, using the truth table, classify each proposition as a tautology, a contingency, or a contradiction. -(I ⊃ ∼I) ⊃ [I ⊃ (I ⊃ ∼I)]

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Question 68

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: \alpha 1 0 For exercises with two propositional variables, the standard assignment is: 1 1 1 0 0 1 0 0 For exercises with three propositional variables, the standard assignment is: \alpha \beta \gamma 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 For exercises with four propositional variables, the standard assignment is: \alpha \beta \gamma \delta 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 Complete truth tables for each of the following propositions. -(D ≡ ∼D) ≡ (∼D ≡ D)

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Question 69

use the following key to determine which of the translations of the given English argument to PL is best. B: Brouwer is an intuitionist. F: Frege is a logicist. G: Gödel is a platonist. H: Hilbert is a formalist. -Hilbert is a formalist if, and only if, Gödel is a platonist. Hilbert is not a formalist and Brouwer is an intuitionist. Hilbert is a formalist if Frege is a logicist. Therefore, Frege is not a logicist and Gödel is not a platonist.

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Question 70

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: \alpha 1 0 For exercises with two propositional variables, the standard assignment is: \alpha 1 1 1 0 0 1 0 0 For exercises with three propositional variables, the standard assignment is: \alpha \beta \gamma 1 1 1 1 1 0 1 0 1 1 0 0e 0 1 1 0 1 0 0 0 1 0 0 0 For exercises with four propositional variables, the standard assignment is: \alpha \gamma \delta\ 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 For each of the given propositions, determine which of the given sequences properly describes the column under the main operator, given the standard assignment of truth values to atomic propositions. -U ? (Z ? U)

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Question 71

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: \alpha 1 0 For exercises with two propositional variables, the standard assignment is: \alpha 1 1 1 0 0 1 0 0 For exercises with three propositional variables, the standard assignment is: \alpha \beta \gamma 1 1 1 1 1 0 1 0 1 1 0 0e 0 1 1 0 1 0 0 0 1 0 0 0 For exercises with four propositional variables, the standard assignment is: \alpha \gamma \delta\ 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 For each of the given propositions, determine which of the given sequences properly describes the column under the main operator, given the standard assignment of truth values to atomic propositions. -A ? [(?B $\lor$ A) ? ?A]

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Question 72

Instructions: For 11-20, use indirect truth tables to determine, for each given set of propositions, whether it is consistent. If the set is consistent, provide a consistent valuation. -L ⊃ M ∼N ⊃ (O $\lor$ L) N $\lor$ P ∼M $\lor$ ∼P

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Question 73

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P • Q) $\lor$ (∼P • Q)] $\lor$ [(P • ∼Q) $\lor$ (∼P • ∼Q)]

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Question 74

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: \alpha 1 0 For exercises with two propositional variables, the standard assignment is: 1 1 1 0 0 1 0 0 For exercises with three propositional variables, the standard assignment is: \alpha \beta \gamma 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 For exercises with four propositional variables, the standard assignment is: \alpha \beta \gamma \delta 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 Complete truth tables for each of the following propositions. -(M $\lor$ N) • (M $\lor$ ?N)

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Question 75

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -G ⊃ (J • ∼K) (I ⊃ H) • G H ⊃ (K $\lor$ I) J • ∼I / I $\lor$ K

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Question 76

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: \alpha 1 0 For exercises with two propositional variables, the standard assignment is: \alpha 1 1 1 0 0 1 0 0 For exercises with three propositional variables, the standard assignment is: \alpha \beta \gamma 1 1 1 1 1 0 1 0 1 1 0 0e 0 1 1 0 1 0 0 0 1 0 0 0 For exercises with four propositional variables, the standard assignment is: \alpha \gamma \delta\ 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 1 For each of the given propositions, determine which of the given sequences properly describes the column under the main operator, given the standard assignment of truth values to atomic propositions. -(K ? L) ? (?K ? L)

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Question 77

Instructions: For questions 11-20, construct complete a truth table for each of the following pairs of propositions. Then, using the truth table, determine whether the statements are logically equivalent or contradictory. If neither, determine whether they are consistent or inconsistent. Justify your answers. -F • (∼G $\lor$ H) and F ≡ (∼H • G)

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Question 78

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: \alpha 1 0 For exercises with two propositional variables, the standard assignment is: 1 1 1 0 0 1 0 0 For exercises with three propositional variables, the standard assignment is: \alpha \beta \gamma 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 For exercises with four propositional variables, the standard assignment is: \alpha \beta \gamma \delta 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 Complete truth tables for each of the following propositions. -[M $\lor$ (N • O)] $\lor$ [(M • N) $\lor$ ∼(M • N)]

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Question 79

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment. For exercises with only one propositional variable, the standard assignment is: \alpha 1 0 For exercises with two propositional variables, the standard assignment is: 1 1 1 0 0 1 0 0 For exercises with three propositional variables, the standard assignment is: \alpha \beta \gamma 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0 For exercises with four propositional variables, the standard assignment is: \alpha \beta \gamma \delta 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 Complete truth tables for each of the following propositions. -[E $\lor$ ?(E • ?F)] ? [F ? ?(E $\lor$ ?F)]

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Question 80

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -A ⊃ B C ⊃∼B ∼A ⊃ D E ⊃∼F ∼E ⊃ G ∼F ⊃ C / D $\lor$ G

Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, specify a counterexample. -X / X $\lor$ [Y ≡ (Z • ∼X)]

construct a complete truth table for each of the following propositions. Then, using the truth table, classify each proposition as a tautology, a contingency, or a contradiction. Justify your answers by appeal to the meanings of those terms. -(I ⊃ ∼I) ⊃ [I ⊃ (I ⊃ ∼I)]

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P $\lor$ Q) ⊃ X] ≡ ∼(P $\lor$ Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(∼P ⊃ P) $\lor$ (P ⊃ A)

For each of the following questions, determine whether the given formula is a wff or not. If it is a wff, indicate its main operator. -{∼R ⊃ [(Q • P) ⊃ S]}

construct a complete truth table for each of the following propositions. Then, using the truth table, classify each proposition as a tautology, a contingency, or a contradiction. -(I ⊃ ∼I) ⊃ [I ⊃ (I ⊃ ∼I)]

Instructions: For 11-20, use indirect truth tables to determine, for each given set of propositions, whether it is consistent. If the set is consistent, provide a consistent valuation. -L ⊃ M ∼N ⊃ (O $\lor$ L) N $\lor$ P ∼M $\lor$ ∼P

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P • Q) $\lor$ (∼P • Q)] $\lor$ [(P • ∼Q) $\lor$ (∼P • ∼Q)]

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -G ⊃ (J • ∼K) (I ⊃ H) • G H ⊃ (K $\lor$ I) J • ∼I / I $\lor$ K

Introducing Logic

Inference in Propositional Logic

Monadic Predicate Logic

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Exam 2: Propositional Logic: Syntax and Semantic

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -A ⊃ B C ⊃∼B ∼A ⊃ D E ⊃∼F ∼E ⊃ G ∼F ⊃ C / D ∨ \lor ∨ G

Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, specify a counterexample. -X / X ∨ \lor ∨ [Y ≡ (Z • ∼X)]

construct a complete truth table for each of the following propositions. Then, using the truth table, classify each proposition as a tautology, a contingency, or a contradiction. Justify your answers by appeal to the meanings of those terms. -(I ⊃ ∼I) ⊃ [I ⊃ (I ⊃ ∼I)]

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P ∨ \lor ∨ Q) ⊃ X] ≡ ∼(P ∨ \lor ∨ Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(∼P ⊃ P) ∨ \lor ∨ (P ⊃ A)

For each of the following questions, determine whether the given formula is a wff or not. If it is a wff, indicate its main operator. -{∼R ⊃ [(Q • P) ⊃ S]}

construct a complete truth table for each of the following propositions. Then, using the truth table, classify each proposition as a tautology, a contingency, or a contradiction. -(I ⊃ ∼I) ⊃ [I ⊃ (I ⊃ ∼I)]

Instructions: For 11-20, use indirect truth tables to determine, for each given set of propositions, whether it is consistent. If the set is consistent, provide a consistent valuation. -L ⊃ M ∼N ⊃ (O ∨ \lor ∨ L) N ∨ \lor ∨ P ∼M ∨ \lor ∨ ∼P

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P • Q) ∨ \lor ∨ (∼P • Q)] ∨ \lor ∨ [(P • ∼Q) ∨ \lor ∨ (∼P • ∼Q)]

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -G ⊃ (J • ∼K) (I ⊃ H) • G H ⊃ (K ∨ \lor ∨ I) J • ∼I / I ∨ \lor ∨ K

Introducing Logic

Inference in Propositional Logic

Monadic Predicate Logic

Full First-Order Logic

Filters

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -A ⊃ B C ⊃∼B ∼A ⊃ D E ⊃∼F ∼E ⊃ G ∼F ⊃ C / D $\lor$ G

Construct a complete truth table for each of the following arguments. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, specify a counterexample. -X / X $\lor$ [Y ≡ (Z • ∼X)]

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P $\lor$ Q) ⊃ X] ≡ ∼(P $\lor$ Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(∼P ⊃ P) $\lor$ (P ⊃ A)

Instructions: For 11-20, use indirect truth tables to determine, for each given set of propositions, whether it is consistent. If the set is consistent, provide a consistent valuation. -L ⊃ M ∼N ⊃ (O $\lor$ L) N $\lor$ P ∼M $\lor$ ∼P

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P • Q) $\lor$ (∼P • Q)] $\lor$ [(P • ∼Q) $\lor$ (∼P • ∼Q)]

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -G ⊃ (J • ∼K) (I ⊃ H) • G H ⊃ (K $\lor$ I) J • ∼I / I $\lor$ K