### Identify the most accurate sentential counterpart

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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"

a. S → (∼B • ∼R)

b. (∼B • ∼R) ∨ S
c. (∼B • ∼R) → S
d. S → ∼(B • R)
e. ∼ (B • R) → S

Question 2. 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"

a. R ∨ G • C
b. R → (G • C)
c. R • (G ∨ C)
d. (G • C) → R
e. R ∨ (G • C)

Question 3. 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"

a. T → (∼M ∨ F)
b. T → ∼ (M ∨ F)
c. T → (∼M ∨∼F)
d. T → ∼(M • F)
e. ∼ (M ∨ F) → T

Question 4. 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"

a. P → T ∨∼N
b.(P → T) ∨∼N
c. (T ∨∼N) → P
d. P → (T ∨∼N)
e. P → (T ∨ N)

Question 5. 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"

a. S • (G ∨ F)
b. (S • G) → F
c. (S • G) ∨ F
d. (S ∨ G) • F
e. S ∨ (G • F)

Question 6. 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"

a. L → ∼ (T • C)
b. ∼ [C • (L → C)]
c. L → (∼T • ∼C)
d.∼ (T • C) → L
e. (∼T • ∼C) → L

Question 7. 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"

a. ∼ (S ∨ T) → P
b. P → (∼S ∨∼T)
c. (∼S ∨∼T) → P
d. (S ∨ T) → P
e. P → ∼(S ∨ T)

Question 8. 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"

a. (∼N ∨∼G) → ∼M
b. (∼N • ∼G) → ∼M
c. ∼ (N ∨ G) → ∼M
d. ∼N ∨ (∼G → ∼M)
e. ∼[ (N ∨ G) → M]

Question 9. 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"

a. (∼L • ∼C) → P
b. P → (∼L • ∼C)
c. P → ∼ (L • C)
d. P → (∼L ∨∼C)
e. P → (L • ∼C)

Question 10. 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"

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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