Step 1: Understanding the Question
We are given two statements and four conclusions. We need to identify the conclusion that can be definitively and logically deduced from the given statements. We must not make any assumptions beyond the information provided.
The statements are:
1. Many business offices are in buildings with 2 to 8 floors. (This sets the context).
2. If a building has more than three floors, it has a lift. (This is a conditional rule: If P, then Q, where P = building has > 3 floors, and Q = building has a lift).
Step 2: Key Formula or Approach
The core of this problem lies in understanding conditional logic (implication). The rule "If P then Q" means that whenever P is true, Q must also be true. It does not say anything about what happens when P is false. We will evaluate each conclusion based on this rule.
Step 3: Detailed Explanation
Let's analyze each conclusion:
Conclusion (a): All floors may be reached by lifts. The statement says the *building* has a lift, not that the lift serves every single floor. Also, a two-floor building might not have a lift at all. The word "may" makes it a possibility, but it's not a logical certainty that follows from the rule. We cannot definitively conclude this. For example, a lift might only go from the ground floor to the top floor.
Conclusion (b): Only floors above the third floor have lifts. This is an incorrect inference. The rule states that a building with, for example, five floors will have a lift. This lift will most likely serve all floors, including the second and third. The condition is about the total number of floors in the building, not about which floors the lift serves. This conclusion is not logically necessary.
Conclusion (c): Seventh floors have lifts. This is a strong and logical deduction. If a building has a seventh floor, it must have at least seven floors in total. Since 7 is greater than 3, the condition "more than three floors" is met. According to the rule, any such building must have a lift. It is a reasonable and logical inference that if a building has a seventh floor and a lift, the lift is meant to provide access to that floor. This conclusion directly follows from the given rule.
Conclusion (d): Second floors do not have lifts. This cannot be concluded. A building with only two or three floors might not have a lift. However, a building with eight floors *will* have a lift, and that lift would almost certainly provide access to the second floor. Since we know such buildings exist (from statement 1), we cannot conclude that second floors never have lifts.
Step 4: Final Answer
Based on the analysis, conclusion (c) is the only one that is a direct and necessary logical consequence of the given statements. If a building has a seventh floor, its total floor count is greater than three, which guarantees the presence of a lift in that building. Therefore, 'Seventh floors have lifts' is the correct conclusion.