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

Quizplus · Accepted Answer

The statement can be translated as follows:
- If Farmers runs an ad or Nationwide cuts costs, then Safeco expands coverage (conditional).
- If Safeco expands coverage, then Geico pays a dividend (conditional).

Using conditional statements, we can combine them to get the answer:

(F ∨ N) ⊃ S  (Conditional 1)
S ⊃ G          (Conditional 2)

To get the conclusion, we apply the law of syllogism:

(F ∨ N) ⊃ G  (Conditional 1 + Conditional 2)

Therefore, the best choice is D.

If Either Farmers Runs an Ad or Nationwide Cuts Costs