In the given question, a statement is given followed by some conclusions. Choose the conclusion(s) which logically follow(s) the given statement.

Statement:
Few shops on this road have neon lights, but they all have signboards.

Conclusions:
I. Some shops have either signboards or neon lights.
II. Some shops have no signboards.
III. Some shops have no neon lights.
IV. Some shops have both signboards and neon lights.

The conclusion(s) correctly drawn is/are:

III and IV

The correct answer is Option 4: III and IV

Statement Analysis:
The statement says:

1. "Few shops on this road have neon lights."
   → This means some shops have neon lights while others do not.
2. "But they all have signboards."
   → This means every shop has a signboard, without exception.

Conclusion Analysis:

1. I. Some shops have either signboards or neon lights.
   → Incorrect.
   The statement specifies that all shops have signboards, so "either" is not applicable.

2. II. Some shops have no signboards.
   → Incorrect.
   The statement clearly says all shops have signboards, so this cannot be true.

3. III. Some shops have no neon lights.
   → Correct.
   The statement says few shops have neon lights, meaning some do not have neon lights.

4. IV. Some shops have both signboards and neon lights.
   → Correct.
   Since few shops have neon lights and all shops have signboards, the shops with neon lights must also have signboards.