Chrysler increases sales only if Honda reduces inventory, provided that Nissan does not lay off workers.
A) (C ≡ H) ⊃ ∼N
B) (C ⊃ H) ⊃ ∼N
C) (H ⊃ C) ⊃ ∼N
D) ∼N ⊃ (H ⊃ C)
E) ∼N ⊃ (C ⊃ H)

Question

Quizplus · Accepted Answer

The statement "Chrysler increases sales only if Honda reduces inventory" can be rewritten as "If Chrysler does not increase sales, then Honda does not reduce inventory." Thus, we have C ⊃ ∼H.

Combining this with "provided that Nissan does not lay off workers" gives ∼N ⊃ (C ⊃ ∼H), which can be rewitten as ∼N ⊃ (H ⊃ C) using contraposition.

Therefore, the best choice is E, which matches this equivalent statement.

Chrysler Increases Sales Only If Honda Reduces Inventory, Provided That