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 :
The core statement is: "Few shops on this road have neon lights, but they all have signboards."
Let's evaluate each conclusion based on the statement:
Since the statement guarantees that all shops have signboards, this conclusion is logically true. Any shop selected will have a signboard, thus fulfilling the "signboards or neon lights" condition.
This directly contradicts the statement that "all shops have signboards". Therefore, Conclusion II is false.
The statement uses "Few shops ... have neon lights". The term "few" implies not all shops have neon lights. Therefore, it logically follows that some shops must not have neon lights. Conclusion III is true.
We know "few shops ... have neon lights" (meaning at least some do) and "all shops have signboards". The shops that have neon lights are part of the total shops on the road. Since all shops have signboards, the specific shops that have neon lights must also have signboards. Therefore, some shops have both. Conclusion IV is true.
Based on the analysis:
Therefore, the conclusions that correctly follow are III and IV.