Seiko has a quartz watch if and only if either Movado does not offer a silver dial or Rado does not have a calendar watch; however, Tissot has luminous hands only if both Fossil is water resistant and Rado has a calendar model.
A) [S ≡ ∼(M ∨ R)] • [T ⊃ (F • R)]
B) [S ≡ (∼M ∨ ∼R)] • [(F • R) ⊃ T]
C) [(∼M ∨ ∼R) ⊃ S] • [T ⊃ (F • R)]
D) [S ≡ (∼M ∨ ∼R)] ∨ [T ⊃ (F • R)]
E) [S ≡ (∼M ∨ ∼R)] • [T ⊃ (F • R)]

Question

Quizplus · Accepted Answer

The statement "Seiko has a quartz watch if and only if either Movado does not offer a silver dial or Rado does not have a calendar watch" can be translated as follows: S if and only if ~ (M v R).
The statement "Tissot has luminous hands only if both Fossil is water resistant and Rado has a calendar model" can be translated as follows: T -> (F & R).
Combining these two statements using the conjunction "and" gives the following logical expression: 
(S iff ~(M v R)) and (T -> (F & R)).
This can be simplified using De Morgan's laws and conditional elimination as follows:
(S iff (~M & ~R)) and (~T v (F & R))
= [(S -> ~M) & (S -> ~R) & (~T v F) & (~T v R)]
= [(~M v ~R v S) & (~T v F) & (~T v R)]
The best choice that matches this expression is E.

Seiko Has a Quartz Watch If and Only If Either