Question 1

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 
A)  True 
B)  False 
C)  Unknown

Question 2

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 3

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 
A)  Tautology 
B)  Contingency 
C)  Contradiction

Question 4

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 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.
-∼X ≡ A

Accepted Answer

A)  True 
B)  False 
C)  Unknown 
A)  True 
B)  False 
C)  Unknown

Question 6

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 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.)
-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 
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

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. 
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.

Question 9

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 10

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 
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

Question 11

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 
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

Question 12

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

Question 13

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 
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

Question 14

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 
A)  True 
B)  False 
C)  Unknown

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 
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

Question 17

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)  Unknown 
A)  True 
B)  False 
C)  Unknown

Question 18

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)
G
F / H 
B)  F ⊃ B B ⊃ (G ⊃ H)
G
F / H 
C)  F ⊃ B B ⊃ (G ≡ H)
G
F / H 
D)  F ⊃ B (B ⊃ G) ⊃ H
G
F / H 
E)  F ⊃ B (B ⊃ H) ⊃ G
G
F / H 
A)  F ⊃ B B ⊃ (H ⊃ G)
G
F / H 
B)  F ⊃ B B ⊃ (G ⊃ H)
G
F / H 
C)  F ⊃ B B ⊃ (G ≡ H)
G
F / H 
D)  F ⊃ B (B ⊃ G) ⊃ H
G
F / H 
E)  F ⊃ B (B ⊃ H) ⊃ G
G
F / H

Question 19

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 $ B
G ≡ B
H / ∼G • H 
B)  ∼F $ \lor $ B
G ≡ B
H / ∼G ≡ H 
C)  ∼(F $ \lor $ 
B) 
G ≡ B
H / ∼G • H 
D)  ∼(F $ \lor $ 
B)  G ≡ B
H / ∼G ⊃ H 
E)  ∼(F $ \lor $ 
B)  G ≡ B
H / H ⊃ ∼G 
A)  ∼F $ \lor $ B
G ≡ B
H / ∼G • H 
B)  ∼F $ \lor $ B
G ≡ B
H / ∼G ≡ H 
C)  ∼(F $ \lor $ 
B) 
G ≡ B
H / ∼G • H 
D)  ∼(F $ \lor $ 
B)  G ≡ B
H / ∼G ⊃ H 
E)  ∼(F $ \lor $ 
B)  G ≡ B
H / H ⊃ ∼G

Question 20

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)]
∼H
B
F $ \lor $ (∼G • 
B)  /∼G 
B)  (F • 
B)  ⊃ (H ⊃ G)
∼H
B
(F $ \lor $ ∼G) • B /∼G 
C)  (F • 
B)  ⊃ (H • G)
∼H
B
F $ \lor $ (G • 
B)  / ∼G 
D)  (F • 
B)  ⊃ (H • G)
∼H
B
(F $ \lor $ ∼G) • B / ∼G 
E)  (F • 
B)  ⊃ (H • G)
∼H
B
F $ \lor $ (∼G • 
B)  / ∼G 
A)  F • [B ⊃ (H • G)]
∼H
B
F $ \lor $ (∼G • 
B)  /∼G 
B)  (F • 
B)  ⊃ (H ⊃ G)
∼H
B
(F $ \lor $ ∼G) • B /∼G 
C)  (F • 
B)  ⊃ (H • G)
∼H
B
F $ \lor $ (G • 
B)  / ∼G 
D)  (F • 
B)  ⊃ (H • G)
∼H
B
(F $ \lor $ ∼G) • B / ∼G 
E)  (F • 
B)  ⊃ (H • G)
∼H
B
F $ \lor $ (∼G • 
B)  / ∼G

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

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)

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)

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

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

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)

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)

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

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)]

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)

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]

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

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)}

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

Introducing Logic

Inference in Propositional Logic

Monadic Predicate Logic

Full First-Order Logic

Filters

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. -(P ⊃ ∼Q) ∨ \lor ∨ ∼P

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)

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)

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

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

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)

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)

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

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)]

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]

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

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)}

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

Introducing Logic

Inference in Propositional Logic

Monadic Predicate Logic

Full First-Order Logic

Filters

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

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)

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

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

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)]

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]

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

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)}