Question 1

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.
-If Frege is a logicist, then Brouwer is an intuitionist. If Brouwer is an intuitionist, then Gödel is a platonist only if Hilbert is a formalist. Gödel is a platonist. Frege is a logicist. So, Hilbert is a formalist.

Accepted Answer

A)   F ⊃ B B ⊃ (H ⊃ G) GF / H
B)   F ⊃ B B ⊃ (G ⊃ H) GF / H
C)   F ⊃ B B ⊃ (G ≡ H) GF / H
D)   F ⊃ B (B ⊃ G)  ⊃ HGF / H
E)   F ⊃ B (B ⊃ H)  ⊃ GGF / HF) B) and D)
G) A) and E)

Question 2

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.
-[(D ⊃ ∼E)  • (F ⊃ E) ] ⊃ [D ⊃ (∼F  ∨ \lor ∨  G) ]

Accepted Answer

A)   It's a wff. The main operator is the first ⊃, reading left to right.
B)   It's a wff. The main operator is the second ⊃, reading left to right.
C)   It's a wff. The main operator is the third ⊃, reading left to right.
D)   It's a wff. The main operator is the fourth ⊃, reading left to right.
E)   Not a wff F) None of the above
G) A) and E)

Question 3

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.
-If Frege is a logicist and Brouwer is an intuitionist, then Hilbert is a formalist and Gödel is a platonist. Hilbert is not a formalist. Brouwer is an intuitionist. Either Frege is a logicist or both Gödel is not a platonist and Brouwer is an intuitionist. Therefore, Gödel is not a platonist.

Accepted Answer

A)   F • [B ⊃ (H • G) ]∼HBF  ∨ \lor ∨  (∼G • 
B)   /∼G
B)   (F • 
B)   ⊃ (H ⊃ G) ∼HB(F  ∨ \lor ∨  ∼G)  • B /∼G
C)   (F • 
B)   ⊃ (H • G) ∼HBF  ∨ \lor ∨  (G • 
B)   / ∼G
D)   (F • 
B)   ⊃ (H • G) ∼HB(F  ∨ \lor ∨  ∼G)  • B / ∼G
E)   (F • 
B)   ⊃ (H • G) ∼HBF  ∨ \lor ∨  (∼G • 
B)   / ∼G F) A) and B)
G) D) and E)

Question 4

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.
-E $ \lor $∼F 
E ⊃∼E
F / E

Accepted Answer

The answer of Construct a complete truth table for each...

Question 5

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.
-∼B ⊃ Y

Accepted Answer

A)   True
B)   False
C)   UnknownD) A) and B)
E) A) and C)

Question 6

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, choose an option which presents a counterexample. (There may be other counterexamples as well.) 
-X  ∨ \lor ∨  Z
X ⊃ (Y  ∨ \lor ∨  Z) 
∼Z ⊃ Y / Y

Accepted Answer

A)   Valid
B)   Invalid. Counterexample when X, Y, and Z are true
C)   Invalid. Counterexample when X is true and Y and Z are false
D)   Invalid. Counterexample when Z is true and X and Y are false
E)   Invalid. Counterexample when X, Y, and Z are false F) A) and D)
G) D) and E)

Question 7

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, choose an option which presents a counterexample. (There may be other counterexamples as well.) 
-P  ∨ \lor ∨  ∼Q
P ⊃ R
∼R / ∼Q

Accepted Answer

A)   Valid
B)   Invalid. Counterexample when P, Q, and R are true
C)   Invalid. Counterexample when P and Q are true and R is false
D)   Invalid. Counterexample when Q and R are true and P is false
E)   Invalid. Counterexample when Q is true and P and R are false F) C) and D)
G) A) and B)

Question 8

use the following key to determine which English sentence best represents the given formula of PL.
A: Peirce studied logic.
B: James was a pluralist.
C: Dewey wrote about thirdness.
D: Dewey denigrated the quest for certainty. 
E: Peirce emphasized education.
-∼(A • E)

Accepted Answer

A)   It is not the case that Peirce either studied logic or emphasized education.
B)   It is not the case that Peirce both studied logic and emphasized education.
C)   Peirce neither studied logic nor emphasized education.
D)   Peirce did not both not study logic and not emphasize education.
E)   Peirce did not study logic and James was not a pluralist.F) None of the above
G) All of the above

Question 9

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.
-It is not the case that either Frege is a logicist or Brouwer is an intuitionist. Gödel being a platonist is necessary and sufficient for Brouwer being an intuitionist. Hilbert is a formalist. So, Gödel is not a platonist; however, Hilbert is a formalist.

Accepted Answer

A)   ∼F  ∨ \lor ∨  BG ≡ BH / ∼G • H
B)   ∼F  ∨ \lor ∨  BG ≡ BH / ∼G ≡ H
C)   ∼(F  ∨ \lor ∨  
B)  G ≡ BH / ∼G • H
D)   ∼(F  ∨ \lor ∨  
B)   G ≡ BH / ∼G ⊃ H
E)   ∼(F  ∨ \lor ∨  
B)   G ≡ BH / H ⊃ ∼G F) None of the above
G) All of the above

Question 10

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.
-∼[(Z ⊃ B)  • (P ⊃ C) ]  ∨ \lor ∨  [(X • Y)  ≡ A]

Accepted Answer

A)   True
B)   False
C)   Unknown D) A) and B)
E) A) and C)

Question 11

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

Accepted Answer

A)   True
B)   False
C)   Unknown D) A) and B)
E) A) and C)

Question 12

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample.
-(P $ \lor $ Q) ⊃ R
(S $ \lor $∼U) ⊃ (∼R • ∼W)
S ⊃ (P • T) / ∼S

Accepted Answer

The answer of use indirect truth tables to determine whether...

Question 13

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.
-Q • (∼A • ∼Q)

Accepted Answer

The answer of Assume A, B, C are true; X,...

Question 14

construct a complete 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.
-R ⊃ (∼S ⊃ R)  and ∼S ⊃ ∼(R  ∨ \lor ∨  ∼R)

Accepted Answer

A)   Logically equivalent
B)   Contradictory
C)   Neither logically equivalent nor contradictory, but consistent
D)   Inconsistent E) B) and C)
F) A) and B)

Question 15

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.
-F • (A ⊃ D)
E $ \lor $∼B
∼[C ⊃ (D $ \lor $ F)] 
A $ \lor $ (B • D)
E ⊃ A

Accepted Answer

The answer of Instructions: For 11-20, use indirect truth tables...

Question 16

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.
-∼{[(H ⊃ I)  ⊃ ∼(I  ∨ \lor ∨  ∼J) ] ⊃ (∼H ⊃ J) }

Accepted Answer

A)   It's a wff. The main operator is the first ∼, reading left to right.
B)   It's a wff. The main operator is the ≡.
C)   It's a wff. The main operator is the second  ∨ \lor ∨ , reading left to right.
D)   It's a wff. The main operator is the •.
E)   Not a wff F) None of the above
G) B) and E)

Question 17

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.
-(C ⊃ ∼D)   ∨ \lor ∨  (∼D ⊃ C)

Accepted Answer

A)   Tautology
B)   Contingency
C)   Contradiction D) A) and B)
E) All of the above

Question 18

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.
-G ⊃ H
∼I ⊃∼G / G ⊃ (H • I)

Accepted Answer

The answer of Construct a complete truth table for each...

Question 19

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.
-∼X ≡ A

Accepted Answer

A)   True
B)   False
C)   UnknownD) All of the above
E) A) and B)

Question 20

use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.) 
-D ⊃ (E  ∨ \lor ∨  F) 
D ⊃ (G  ∨ \lor ∨  F) 
∼(F  ∨ \lor ∨  H)  / D ⊃ (E • G)

Accepted Answer

A)   Valid
B)   Invalid. Counterexample when D, E and F are true and G and H are false
C)   Invalid. Counterexample when D and E are true and F, G, and H are false
D)   Invalid. Counterexample when D, G, and H are true and E and F are false
E)   Invalid. Counterexample when D and G are true and E, F, and H are false F) None of the above
G) B) and D)

Exam 2: Propositional Logic: Syntax and Semantic

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. -∼[(Z ⊃ B) • (P ⊃ C) ] $\lor$ [(X • Y) ≡ A]

Correct Answer
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Correct Answer
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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. -∼X ≡ A

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Correct Answer
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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. -E $\lor$ ∼F E ⊃∼E F / E

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use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.) -D ⊃ (E $\lor$ F) D ⊃ (G $\lor$ F) ∼(F $\lor$ H) / D ⊃ (E • G)

Correct Answer
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use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -(P $\lor$ Q) ⊃ R (S $\lor$ ∼U) ⊃ (∼R • ∼W) S ⊃ (P • T) / ∼S

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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

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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. -(C ⊃ ∼D) $\lor$ (∼D ⊃ C)

Correct Answer
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Correct Answer
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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. -G ⊃ H ∼I ⊃∼G / G ⊃ (H • I)

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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. -∼B ⊃ Y

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Correct Answer
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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. -F • (A ⊃ D) E $\lor$ ∼B ∼[C ⊃ (D $\lor$ F)] A $\lor$ (B • D) E ⊃ A

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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. -Q • (∼A • ∼Q)

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Correct Answer
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use the following key to determine which English sentence best represents the given formula of PL. A: Peirce studied logic. B: James was a pluralist. C: Dewey wrote about thirdness. D: Dewey denigrated the quest for certainty. E: Peirce emphasized education. -∼(A • E)

Correct Answer
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Correct Answer
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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. -∼{[(H ⊃ I) ⊃ ∼(I $\lor$ ∼J) ] ⊃ (∼H ⊃ J) }

Correct Answer
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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. -[(D ⊃ ∼E) • (F ⊃ E) ] ⊃ [D ⊃ (∼F $\lor$ G) ]

Correct Answer
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Exam 2: Propositional Logic: Syntax and Semantic

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. -∼[(Z ⊃ B) • (P ⊃ C) ] ∨ \lor ∨ [(X • Y) ≡ A]

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Correct AnswerverifiedShow Answer

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. -∼X ≡ A

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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. -E ∨ \lor ∨ ∼F E ⊃∼E F / E

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use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -(P ∨ \lor ∨ Q) ⊃ R (S ∨ \lor ∨ ∼U) ⊃ (∼R • ∼W) S ⊃ (P • T) / ∼S

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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

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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. -(C ⊃ ∼D) ∨ \lor ∨ (∼D ⊃ C)

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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. -G ⊃ H ∼I ⊃∼G / G ⊃ (H • I)

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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. -∼B ⊃ Y

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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. -F • (A ⊃ D) E ∨ \lor ∨ ∼B ∼[C ⊃ (D ∨ \lor ∨ F)] A ∨ \lor ∨ (B • D) E ⊃ A

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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. -Q • (∼A • ∼Q)

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use the following key to determine which English sentence best represents the given formula of PL. A: Peirce studied logic. B: James was a pluralist. C: Dewey wrote about thirdness. D: Dewey denigrated the quest for certainty. E: Peirce emphasized education. -∼(A • E)

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Correct AnswerverifiedShow Answer

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. -∼{[(H ⊃ I) ⊃ ∼(I ∨ \lor ∨ ∼J) ] ⊃ (∼H ⊃ J) }

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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. -[(D ⊃ ∼E) • (F ⊃ E) ] ⊃ [D ⊃ (∼F ∨ \lor ∨ G) ]

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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. -∼[(Z ⊃ B) • (P ⊃ C) ] $\lor$ [(X • Y) ≡ A]

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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. -E $\lor$ ∼F E ⊃∼E F / E

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Correct Answer
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use indirect truth tables to determine whether each of the following arguments is valid. If the argument is invalid, specify a counterexample. -(P $\lor$ Q) ⊃ R (S $\lor$ ∼U) ⊃ (∼R • ∼W) S ⊃ (P • T) / ∼S

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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

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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. -(C ⊃ ∼D) $\lor$ (∼D ⊃ C)

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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. -F • (A ⊃ D) E $\lor$ ∼B ∼[C ⊃ (D $\lor$ F)] A $\lor$ (B • D) E ⊃ A

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Correct Answer
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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. -∼{[(H ⊃ I) ⊃ ∼(I $\lor$ ∼J) ] ⊃ (∼H ⊃ J) }

Correct Answer
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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. -[(D ⊃ ∼E) • (F ⊃ E) ] ⊃ [D ⊃ (∼F $\lor$ G) ]

Correct Answer
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