Step-by-step Solution:

Logical Deduction

First, let's establish a clear map of the roads from West to East by placing road B at a reference point of 0.

1. "B is 1/2 km West of C" places C at position 0.5.


2. "E is between B and C" means E's position is between 0 and 0.5.


3. "A is 1 km East of B" places A at position 1.


4. "D is 1 km West of E" means D's position is E - 1. (So D must be between -1 and -0.5).

Our final map from West to East is:

    D (between -1 and -0.5)
    B (at 0)
    E (between 0 and 0.5)
    C (at 0.5)
    A (at 1)

Evaluation of the Statements

• 
  A. D is 2 km West of A: The distance between A (at 1) and D is 1 - D. Since D is between -1 and -0.5, the distance is always less than 2 km. This statement is False.
  


• 
  B. C is less than 1.5 km from D: The distance between C (at 0.5) and D is 0.5 - D. The distance is always less than 1.5 km. This statement is True.
  


• 
  D. E is less than 1 km from A: The distance between A (at 1) and E is 1 - E. The distance is always less than 1 km. This statement is True.
  

Final Answer: The only statement that is necessarily false is A.