Deck 6: Propositional Logic

Question 1

Thrifty's laying off workers is a sufficient condition for National's improving efficiency, if Enterprise reorganizes.

A) E ⊃ (N ⊃ T)
B) (T ⊃ N) ⊃ E
C) E ⊃ (T ⊃ N)
D) T ⊃ (N ⊃ E)
E) E ≡ (T ⊃ N)

Answer 1

E ⊃ (T ⊃ N)

Question 2

Statement 2I
Given the following statement:
(L • ∼ E) ≡ (E • ∼ L)
Statement 2I is:

A) Self-contradictory.
B) Tautologous.
C) Consistent.
D) Contingent.
E) Inconsistent.

Answer 2

Contingent.

Question 3

In Proposition 2I, the main operator is a:

A) Tilde.
B) Wedge.
C) Horseshoe.
D) Triple bar.
E) Dot.

Answer 3

Triple bar.

Question 4

If National's improving efficiency implies that Enterprise reorganizes, then Avis buys new cars.

A) (N ⊃ E ⊃ A)
B) N ⊃ (E ⊃ A)
C) (N ⊃ E) ⊃ A
D) A ⊃ (N ⊃ E)
E) (E ⊃ N) ⊃ A

Question 5

In Proposition 1I, the main operator is a:

A) Dot.
B) Tilde.
C) Horseshoe.
D) Triple bar.
E) Wedge.

Question 6

The truth table for Statement 1I has how many lines?

A) Two.
B) Eight.
C) Four.
D) Six.
E) Nine.

Question 7

Statement 1I
Given the following statement:
(G • ∼ M) ⊃ (M ∨ G)
Statement 1I is:

A) Consistent.
B) Logically equivalent.
C) Tautologous.
D) Contingent.
E) Self-contradictory.

Question 8

The truth table for Statement 3I has how many lines?

A) Six.
B) Nine.
C) Eleven.
D) Eight.
E) Four.

Question 9

Statement 3I
Given the following statement:
[K • (P ∨ ∼ R)] • [K ⊃ (R • ∼ P)]
Statement 3I is:

A) Valid.
B) Self-contradictory.
C) Tautologous.
D) Inconsistent.
E) Contingent.

Question 10

Budget lowers rates unless Hertz and Thrifty do not overhaul operations.

A) B ∨ (∼H • ∼T)
B) B ∨ ∼(H • T)
C) B ⊃ (∼H • ∼T)
D) (∼H • ∼T) ⊃ B
E) (B ∨ ∼H) • ∼T

Question 11

Budget's lowering rates implies that Hertz runs a sale, only if Avis does not buy new cars.

A) (B ⊃ H) ⊃ ∼A
B) ∼A ⊃ (B ⊃ H)
C) (B ⊃ H) ≡ ∼A
D) (H ⊃ B) ⊃ ∼A
E) (B ⊃ H ⊃ A)

Question 12

Hertz's running a sale and Budget's lowering rates are a necessary condition for either Avis's buying new cars or Thrifty's laying off workers.

A) (A • T) ⊃ (H ∨ B)
B) (H • B) ⊃ (A ∨ T)
C) (H • B) ∨ (A ∨ T)
D) (A ∨ T) ⊃ (H • B)
E) (H • B) ≡ (A ∨ T)

Question 13

Proposition 1I
Given the following proposition:
[(B ≡ ∼ Y) • ∼(∼ X ⊃ A)] ∨ [∼(X ≡ A) ⊃ (Y • ∼ A)]
Given that A and B are true and X and Y are false, determine the truth value of Proposition 1I.

Question 14

National does not improve efficiency or Enterprise does not reorganize, given that Thrifty lays off workers.

A) T ⊃ ∼(N ∨ E)
B) (∼N ∨ ∼E) ⊃ T
C) ∼(N ∨ E) ⊃ T
D) (T ⊃ ∼N) ∨ ∼E
E) T ⊃ (∼N ∨ ∼E)

Question 15

Proposition 2I
Given the following proposition:
[∼(X ∨ B) ≡ (∼ Y ⊃ ∼ X)] ≡ ∼[(A ⊃ ∼ Y) • ∼(∼ X ⊃ ∼ B)]
Given that A and B are true and X and Y are false, determine the truth value of Proposition 2I.

Question 16

Given the pair of statements: R ∨ S and S ⊃ ∼ R
These statements are:

A) Inconsistent.
B) Contradictory.
C) Invalid.
D) Logically equivalent.
E) Consistent.

Question 17

Hertz runs a sale or both Avis buys new cars and Budget lowers rates.

A) H ∨ A • B
B) H ∨ (A • B)
C) (H ∨ A) • B
D) H • (A ∨ B)
E) H • A ∨ B

Question 18

Not both Hertz runs a sale and Thrifty lays off workers if either Avis buys new cars or Budget lowers rates.

A) (∼H • ∼T) ⊃ (A ∨ B)
B) (A ∨ B) ⊃ (∼H • ∼T)
C) ∼(H • T) ⊃ (A ∨ B)
D) (A ∨ B) ⊃ ∼(H • T)
E) (A • B) ⊃ ∼(H ∨ T)

Question 19

National's improving efficiency or Enterprise's reorganizing is a sufficient and necessary condition for Thrifty's laying off workers, provided that Avis buys new cars.

A) (N ∨ E) ≡ (A ⊃ T)
B) A ⊃ [(N ∨ E) ≡ T]
C) [(N ∨ E) ≡ T] ⊃ A
D) A ⊃ [(N ⊃ E) • (E ⊃ N)]
E) A ≡ [(N ∨ E) ⊃ T]

Question 20

Thrifty lays off workers only if neither National improves efficiency nor Enterprise reorganizes.

A) T ⊃ ∼(N ∨ E)
B) ∼(N ∨ E) ⊃ T
C) T ⊃ (∼N ∨ ∼T)
D) (∼N ∨ ∼E) ⊃ T
E) T ≡ ∼(N ∨ E)

Question 21

∼G ∨ ∼B

A) Disjunctive syllogism.
B) Invalid.
C) Denying the antecedent.
D) Affirming the consequent.
E) Modus tollens.

Question 22

S ⊃ ∼C

A) Modus tollens.
B) Affirming the consequent.
C) Denying the antecedent.
D) Modus ponens.
E) Invalid.

Question 23

Given the argument: S ⊃ E / N ⊃ (∼ S ⊃ E) // N ⊃ E
This argument is:

A) Invalid; fails in 5th line.
B) Invalid; fails in 6th line.
C) Valid.
D) Invalid; fails in 2nd line.
E) Invalid; fails in 3rd line.

Question 24

In the expression 'P • Q', 'P' is called:

A) A conjunction.
B) A disjunct.
C) An antecedent.
D) A conjunct.
E) A disjunction.

Question 25

E ⊃ ∼T

A) Modus ponens.
B) Constructive dilemma.
C) Pure hypothetical syllogism.
D) Invalid.
E) Disjunctive syllogism.

Question 26

∼Q ∨ S

A) Disjunctive syllogism.
B) Modus ponens.
C) Invalid.
D) Modus tollens.
E) Denying the antecedent.

Question 27

Given the statements: W ⊃ (E ∨ ∼ G) / A ⊃ (G ∨ ∼ E) / H ⊃ (A • W) / H • E
These statements are:

A) Inconsistent.
B) Tautologous.
C) Invalid.
D) Logically equivalent.
E) Consistent.

Question 28

If a group of statements are consistent, this means:

A) At least one of them is true.
B) It is possible for all of them to be true.
C) At least one of them is false.
D) All of them are true.
E) It is possible for all of them to be false.

Question 29

Given the argument: K ∨ B / K ≡ (D ∨ ∼ B) // K ⊃ D
This argument is:

A) Invalid; fails in 1st line.
B) Invalid; fails in 2nd line.
C) Valid.
D) Invalid; fails in 4th line.
E) Invalid; fails in 3rd line.

Question 30

Given the statements: ∼ S ⊃ D / K ⊃ S / D ⊃ K / R ≡ ∼(S • C) / R ≡ C
These statements are:

A) Contradictory.
B) Tautologous.
C) Consistent.
D) Inconsistent.
E) Valid.

Question 31

Given the argument: G ⊃ (N • E) / H ⊃ N / K ⊃ ∼E / (H • K) ≡ G
This argument is:

A) Valid.
B) Invalid.
C) Uncogent.
D) Cogent.
E) Sound.

Question 32

(M ⊃ ∼T) • (∼H ⊃ T)

A) Invalid.
B) Destructive dilemma.
C) Constructive dilemma
D) Modus tollens.
E) Affirming the consequent.

Question 33

According to De Morgan's rule, ∼(P • Q) is logically equivalent to:

A) P ∨ Q
B) ∼P • ∼Q
C) ∼P ∨ ∼Q
D) P • Q
E) P ≡ Q

Question 34

Given the argument: J ⊃ (E • Q) / ∼ Q ⊃ L / (E ∨ M) ⊃ (L ∨ ∼ Q) / M ∨ J // L
This argument is:

A) Valid.
B) Invalid.
C) Sound.
D) Cogent.
E) Uncogent.

Question 35

Given the pair of statements: (H • J) ∨ (N • J) and (N ∨ H) ⊃ ∼ J
These statements are:

A) Contradictory.
B) Valid.
C) Logically equivalent.
D) Consistent.
E) Inconsistent.

Question 36

(∼W ⊃ L) • (N ⊃ ∼R)

A) Invalid.
B) Pure hypothetical syllogism.
C) Destructive dilemma.
D) Denying the antecedent.
E) Constructive dilemma.

Question 37

K

A) Disjunctive syllogism.
B) Invalid.
C) Denying the antecedent.
D) Modus tollens.
E) Affirming the consequent.

Question 38

F ⊃ ∼H

A) Pure hypothetical syllogism.
B) Constructive dilemma.
C) Invalid.
D) Affirming the consequent.
E) Disjunctive syllogism.

Question 39

R

A) Invalid.
B) Affirming the consequent.
C) Disjunctive syllogism.
D) Modus tollens.
E) Modus ponens.

Question 40

∼F ⊃ L

A) Denying the antecedent.
B) Modus ponens.
C) Affirming the consequent.
D) Modus tollens.
E) Invalid.

Question 41

Statement 1H
Given the following statement:
(S ⊃ ∼ R) ⊃ (∼ S • R)
The truth table for Statement 1H has how many lines?

A) Two.
B) Eight.
C) Four.
D) Six.
E) Nine.

Question 42

Statement 1H
Given the following statement:
(S ⊃ ∼ R) ⊃ (∼ S • R)
Statement 1H is:

A) Consistent.
B) Logically equivalent.
C) Tautologous.
D) Contingent.
E) Self-contradictory.

Question 43

Statement 2H
Given the following statement:
[N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)]
Statement 2H is:

A) Inconsistent.
B) Contingent.
C) Consistent.
D) Self-contradictory.
E) Tautologous.

Question 44

United's lowering fares is a sufficient and necessary condition for American's hiring pilots, given that Frontier does not improve service.

A) (U ≡ A) ⊃ ∼F
B) ∼F ⊃ (U ≡ A)
C) (∼F ⊃ U) • (∼F ⊃ A)
D) (∼F ≡ U) • (∼F ≡ A)
E) ∼F ≡ (U ⊃ A)

Question 45

Proposition 2H
Given the following proposition:
∼[(B • ∼X) ⊃ ∼(Y ≡ ∼B)] ⊃ [∼(X ⊃ A) ∨ (B ⊃ ∼Y)]
Given that A and B are true and X and Y are false, determine the truth value of Proposition 2H.

Question 46

The wedge operator is used to translate:

A) "Nevertheless."
B) "Moreover."
C) "Unless."
D) "Implies."
E) "Provided that."

Question 47

Frontier's improving service is a necessary condition for either JetBlue's buying planes or United's lowering fares.

A) F ≡ (J ∨ U)
B) F ⊃ (J ∨ U)
C) (F ⊃ J) • (F ⊃ U)
D) (J ∨ U) ⊃ F
E) (J ⊃F) ∨ (F ⊃ U)

Question 48

American's hiring pilots is a sufficient condition for both Delta's advertising a sale and Southwest's expanding routes.

A) (D • S) ∨ A
B) (D ⊃ A) • (S ⊃ A)
C) (D • S) ⊃ A
D) A ⊃ (D • S)
E) A ≡ (D • S)

Question 49

Proposition 1H
Given the following proposition:
[(A ≡ ∼B) ∨ (X ⊃ Y)] • [(Y ⊃ A) ≡ ∼(X ∨ B)]
In Proposition 1H, the main operator is a:

A) Horseshoe.
B) Tilde.
C) Dot.
D) Triple bar.
E) Wedge.

Question 50

Frontier's improving service implies that not both JetBlue buys planes and Southwest expands routes.

A) F ⊃ ∼(J ∨ S)
B) F ⊃ (∼J • ∼S)
C) F ⊃ ∼(J • S)
D) (F ⊃ ∼J) • S
E) F ≡ ∼(J • S)

Question 51

If an indirect truth table requiring more than one line is constructed for either an argument or a series of statements and a contradiction is derived on the first line, then:

A) The second line must be completed.
B) The argument is valid and the statements are consistent.
C) The argument is valid and the statements are inconsistent.
D) The argument is invalid and the statements are consistent.
E) The argument is invalid and the statements are inconsistent.

Question 52

Proposition 2H
Given the following proposition:
∼[(B • ∼X) ⊃ ∼(Y ≡ ∼B)] ⊃ [∼(X ⊃ A) ∨ (B ⊃ ∼Y)]
In Proposition 2H, the main operator is a:

A) Dot.
B) Wedge.
C) Triple bar.
D) Tilde.
E) Horseshoe.

Question 53

JetBlue buys planes if and only if both Delta does not advertise a sale and Southwest does not expand routes.

A) J ≡ ∼(D • S)
B) J ⊃ (∼D • ∼S)
C) J ≡ (∼D • ∼S)
D) ∼(D ∨ S) ⊃ J
E) J ∨ (∼D • ∼S)

Question 54

Delta advertises a sale and either United lowers fares or American hires pilots.

A) D • (U ∨ A)
B) D ∨ (U • A)
C) D • U ∨ A
D) (D • U) ∨ A
E) D ∨ (U • A).

Question 55

Statement 2H
Given the following statement:
[N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)]
The truth table for Statement 2H has how many lines?

A) Five.
B) Nine.
C) Eight.
D) Six.
E) Four.

Question 56

Southwest expands routes if either American does not hire pilots or United does not lower fares.

A) ∼(A ∨ U) ⊃ S
B) (∼A • ∼U) ⊃ S
C) S ⊃ (∼A ∨ ∼U)
D) (S ⊃ ∼A ∨ ∼U)
E) (∼A ∨ ∼U) ⊃ S

Question 57

Proposition 1H
Given the following proposition:
[(A ≡ ∼B) ∨ (X ⊃ Y)] • [(Y ⊃ A) ≡ ∼(X ∨ B)]
Given that A and B are true and X and Y are false, determine the truth value of Proposition 1H.

Question 58

United lowers fares if and only if both JetBlue buys planes and Delta advertises a sale, provided that American hires pilots.

A) (U ≡ A) • (J ≡ D)
B) A ⊃ [U ≡ (J • D)]
C) [U ≡ (J • D)] ⊃ A
D) A ⊃ [(U ⊃ J) • (D ⊃ U]
E) [U ⊃ (J • D)] ⊃ A

Question 59

JetBlue buys planes if Delta advertises a sale, and Frontier improves service only if Southwest expands routes.

A) (D ⊃ J) • (F ⊃ S)
B) (D ≡ J) • (F ≡ S)
C) (J ⊃ D) • (S ⊃ F)
D) (D • J) ⊃ (S • F)
E) (J ⊃ D) • (F ⊃ S)

Question 60

JetBlue buys planes unless neither Frontier improves service nor United lowers fares.

A) J ∨ ∼(F • U)
B) J ∨ ∼(F ∨ U)
C) J ∨ (∼F ∨ ∼U)
D) J ⊃ ∼(F ∨ U)
E) ∼(F ∨ U) ⊃ J

Question 61

(K ⊃ ∼A) • (S ⊃ ∼D)

A) Invalid.
B) Modus tollens.
C) Affirming the consequent.
D) Denying the antecedent.
E) Destructive dilemma.

Question 62

Given the statement: (E ∨ ∼ H) • (H • ∼ E)
This statement is:

A) Valid.
B) Self-contradictory.
C) Tautologous.
D) Inconsistent.
E) Contingent.

Question 63

(∼N ⊃ R) • (F ⊃ ∼G)

A) Constructive dilemma.
B) Invalid.
C) Denying the antecedent.
D) Modus tollens.
E) Destructive dilemma.

Question 64

B ⊃ ∼Q Q
∼B

A) Modus ponens.
B) Modus tollens.
C) Disjunctive syllogism.
D) Invalid.
E) Denying the antecedent.

Question 65

Given the argument: M ⊃ J / ∼ J ⊃ R // (M ∨ ∼ R) ⊃ J
This argument is:

A) Invalid; fails in 3rd line.
B) Invalid; fails in 2nd line.
C) Invalid; fails in 4th line.
D) Invalid; fails in 1st line.
E) Valid.

Question 66

D ⊃ ∼N

A) Affirming the consequent.
B) Invalid.
C) Denying the antecedent.
D) Modus ponens.
E) Modus tollens.

Question 67

∼P ∨ M

A) Modus tollens.
B) Denying the antecedent.
C) Pure hypothetical syllogism.
D) Disjunctive syllogism.
E) Invalid.

Question 68

Given the statements: H ⊃ E / M ⊃ R / (M • E) ⊃ G / (R • G) ⊃ E / M ∨ E
These statements are:

A) Invalid.
B) Tautologous.
C) Consistent.
D) Logically equivalent.
E) Inconsistent.

Question 69

Given the pair of statements: G ⊃ (W • ∼ Q) and (W ∨ ∼ G) • ∼(Q • G)
These statements are:

A) Inconsistent.
B) Contradictory.
C) Invalid.
D) Logically equivalent.
E) Consistent.

Question 70

In the expression 'P ∨ Q', 'P' is called:

A) A disjunction.
B) A conjunct.
C) A disjunct.
D) A conjunction.
E) An antecedent.

Question 71

Given the statements: C ⊃ L / K ⊃ ∼H / L ⊃ (N ⊃ K) / C ⊃ (H ⊃ N) / C • H
These statements are:

A) Contradictory.
B) Tautologous.
C) Consistent.
D) Inconsistent.
E) Valid.

Question 72

Given the argument: R ⊃ (H • ∼N) / (H • ∼B) ⊃ (N ∨ ∼P) / K ⊃ (G • P) // (K • R) ⊃ B
This argument is:

A) Invalid.
B) Valid.
C) Uncogent.
D) Cogent.
E) Sound.

Question 73

∼H ⊃ ∼B

A) Denying the antecedent.
B) Invalid.
C) Pure hypothetical syllogism.
D) Constructive dilemma.
E) Destructive dilemma.

Question 74

Given the argument: S ⊃ W / C ⊃ L / (M • ∼L) ∨ (D • ∼W) / C ∨ S // D • M
This argument is:

A) Invalid.
B) Cogent.
C) Sound.
D) Valid.
E) Uncogent.

Question 75

∼L ⊃ F

A) Disjunctive syllogism.
B) Denying the antecedent.
C) Modus tollens.
D) Modus ponens.
E) Invalid.

Question 76

Given the argument: Q ⊃ A / ∼ (A • Q) / A ≡ Q
This argument is:

A) Invalid; fails in 1^st line.
B) Valid.
C) Invalid; fails in 3^rd line.
D) Invalid; fails in 2^nd line.
E) Invalid; fails in 4^th line.

Question 77

Given the pair of statements: P • ∼ Z and Z ≡ P
These statements are:

A) Inconsistent.
B) Valid.
C) Contradictory.
D) Consistent.
E) Logically equivalent.

Question 78

S ⊃ ∼R

A) Disjunctive syllogism.
B) Constructive dilemma.
C) Pure hypothetical syllogism.
D) Affirming the consequent.
E) Invalid.

Question 79

G ∨ ∼T

A) Invalid.
B) Disjunctive syllogism.
C) Modus ponens.
D) Affirming the consequent.
E) Modus tollens.

Question 80

∼G

A) Constructive dilemma.
B) Disjunctive syllogism.
C) Modus ponens.
D) Denying the antecedent.
E) Invalid.