Natural language proposition 1

Natural language proposition

Q1…Identify the most accurate sentential counterpart to the natural language proposition

“If Smith increases enrollment, then both Baylor and Rice do not raise tuition.”

S = “Smith increases enrollment”; B = “Baylor raises tuition”; R = “Rice raises tuition”

Select one:

a. 

S → (∼B • ∼R)

b. 

(∼B • ∼R) ∨ S

c. 

(∼B • ∼R) → S

d. 

S → ∼(B • R)

e. 

∼ (B • R) → S

Question 2

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Identify the most accurate sentential counterpart to the natural language proposition.

“Either Redbook increases circulation or both Glamour hires models and Cosmo raises its price.”

R = “Redbook increases circulation”; G = “Glamour hires models”; C = “Cosmo raises its price”

Select one:

a. 

R ∨ G • C

b. 

R → (G • C)

c. 

R • (G ∨ C)

d. 

(G • C) → R

e. 

R ∨ (G • C)

Question 3

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Identify the most accurate sentential counterpart to the natural language proposition.

“If Time expands coverage, then neither Money hires new writers nor Forbes solicits new advertisers.”

T = “Time expands coverage”; M = “Money hires new writers”; F = “Forbes solicits new advertisers”

Select one:

a. 

T → (∼M ∨ F)

b. 

T → ∼ (M ∨ F)

c. 

T → (∼M ∨ ∼F)

d. T → ∼(M • F)

e. ∼ (M ∨ F) → T

Question 4

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Identify the most accurate sentential counterpart to the natural language proposition.

“If People raises its price, then either Time expands coverage or Newsweek does not increase circulation.”

P = “People raises its prices”; T = “Time expands coverage”; N = “Newsweek increases circulation”

Select one:

a. P → T ∨ ∼N

b.

(P → T) ∨ ∼N

c. (T ∨ ∼N) → P

d.

P → (T ∨ ∼N)

e.

P → (T ∨ N)

Question 5

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Identify the most accurate sentential counterpart to the natural language proposition.

“Either Safeco reduces premiums and Geico cuts costs or Farmers hires agents.”

S = “Safeco reduces premiums”; G = “Geico cuts costs”; F = “Farmers hires agents”

Select one:

a. S • (G ∨ F)

b. (S • G) → F

c.

(S • G) ∨ F

d. (S ∨ G) • F

e.

S ∨ (G • F)

Question 6

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Identify the most accurate sentential counterpart to the natural language proposition.

“If Liberty opens new offices, then not both Travelers and Conseco run an ad.”

L = “Liberty opens new offices”; T = “Travelers runs an ad; C = “Conseco runs an ad”

Select one:

a. L → ∼ (T • C)

b. ∼ [C • (L → C)]

c. 

L → (∼T • ∼C)

d.

∼ (T • C) → L

e.

(∼T • ∼C) → L

Question 7

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Identify the most accurate sentential counterpart to the natural language proposition.

“If neither Safeco cuts costs nor Travelers runs an ad, then Progressive increases its territory.”

S = “Safeco cuts costs”; T = “Travelers runs an ad”; P = “Progressive increases its territory”

Select one:

a. ∼ (S ∨ T) → P

b. 

P → (∼S ∨ ∼T)

c. 

(∼S ∨ ∼T) → P

d. 

(S ∨ T) → P

e. P → ∼(S ∨ T)

Question 8

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Identify the most accurate sentential counterpart to the natural language proposition.

“If either Nationwide or Geico does not open new offices, then Metropolitan does not hire agents.”

N = “Nationwide opens new offices”; G = “Geico opens new offices”; M = “Metropolitan hires agents”

Select one:

a. 

(∼N ∨ ∼G) → ∼M

b. 

(∼N • ∼G) → ∼M

c. 

∼ (N ∨ G) → ∼M

d. 

∼N ∨ (∼G → ∼M)

e. 

∼[ (N ∨ G) → M]

Question 9

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Identify the most accurate sentential counterpart to the natural language proposition.

“If Progressive expands coverage then both Liberty and Conseco do not cut costs.”

P = “Progressive expands coverage”; L = “Liberty cuts costs”; C = “Conseco cuts costs”

Select one:

a. 

(∼L • ∼C) → P

b. 

P → (∼L • ∼C)

c. 

P → ∼ (L • C)

d. 

P → (∼L ∨ ∼C)

e. 

P → (L • ∼C)

Question 10

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Identify the most accurate sentential counterpart to the natural language proposition.

“If either Farmers runs an ad or Nationwide cuts costs, then if Safeco expands coverage then Geico pays a dividend.”

F = “Farmers run an ad”; N = “Nationwide cuts costs”; S = “Safeco expands coverage”; G = “Geico pays dividends”

Select one:

a. 

(F ∨ N) → (G → S)

b. 

[F → (S → G)] ∨ [N → (S → G)]

c. 

[(F ∨ N) → S] → G

d. 

(F ∨ N) → (S → G)

e. 

F ∨ [N → (S → G)]

Question 11

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Determine the argument form below:

1. H → ∼ M

2. M           

3. ∼ H

Select one:

a. modus ponens

b. modus tollens

c. disjunctive syllogism

d. hypothetical syllogism

e. constructive dilemma

f. destructive dilemma

g. affirming the consequent

h. denying the antecedent

Question 12

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Determine the argument form below:

1. ∼ D → N

2. D           

3. ∼N

Select one:

a. modus ponens

b. modus tollens

c. disjunctive syllogism

d. hypothetical syllogism 

e. constructive dilemma

f. destructive dilemma

g. affirming the consequent

h. denying the antecedent

Question 13

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Determine the argument form below:

1. ∼ S

2. ∼ S → F

3. F

Select one:

a. modus ponens

b. modus tollens

c. disjunctive syllogism

d. hypothetical syllogism

e. constructive dilemma

f. destructive dilemma

g. affirming the consequent 

h. denying the antecedent

Question 14

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Determine the argument form below:

1. S ∨ ∼T

2. ∼ S      

3. ∼ T

Select one:

a. modus ponens

b. modus tollens

c. disjunctive syllogism

d. hypothetical syllogism

e. constructive dilemma

f. destructive dilemma

g. affirming the consequent

h. denying the antecedent

Question 15

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Determine the argument form below:

1. ∼J → C

2. C → ∼T

3. ∼J → ∼T

Select one:

a. modus ponens

b. modus tollens

c. disjunctive syllogism

d. hypothetical syllogism

e. constructive dilemma

f. destructive syllogism

g. affirming the consequent 

h. denying the antecedent

Question 16

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Determine the argument form below:

1. L

2. ∼N → L

3. ∼N

Select one:

a. modus ponens 

b. modus tollens

c. disjunctive syllogism

d. hypothetical syllogism

e. constructive dilemma

f. destructive dilemma

g. affirming the consequent

h. denying the antecedent

Question 17

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Determine the argument form below:

1. G ∨ ∼T

2. (G → ∼H) • (∼T → A)

3. ∼H ∨ A

Select one:

a. modus ponens

b. modus tollens

c. disjunctive syllogism

d. hypothetical syllogism

e. constructive dilemma

f. destructive dilemma

g. affirming the consequent

h. denying the antecedent

Question 18

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Determine the argument form below:

1. K ∨ ∼B

2. B         

3. K

Select one:

a. modus ponens

b. modus tollens

c. disjunctive syllogism

d. hypothetical syllogism

e. constructive dilemma

f. destructive dilemma

g. affirming the consequent

h. denying the antecedent

Question 19

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Determine the argument form below:

1. [P ∨ (D → T)] → ∼ (C • R)

2. [P ∨ (D → T)]                   

3. ∼ (C • R)

Select one:

a. modus ponens

b. modus tollens

c. disjunctive syllogism

d. hypothetical syllogism

e. constructive dilemma

f. destructive dilemma

g. affirming the consequent

h. denying the antecedent

Question 20

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Determine the argument form below:

1. (T → W) → [K • (E → Q)]

2. ∼ [K • (E → Q)]                

3. ∼ (T → W)

Select one:

a. modus ponens

b. modus tollens

c. disjunctive syllogism