Consider the following statements about states, dams, and water problems. Treat the statements as logically true and then decide which conclusions definitely follow. Statement: All states that have dams face no water problem. Statement: One of the states has no dam. Conclusions: I. The state without a dam may be facing a water problem. II. Dams solve the water problem of a state.

Introduction / Context:
This statement and conclusion question connects the presence of dams in a state with the absence of water problems. You must interpret the statements in a purely logical manner and then evaluate the given conclusions. The question also introduces the phrase may be, which expresses possibility rather than certainty. Understanding how possibility based conclusions behave in logical reasoning is important here.

Given Data / Assumptions:
- Any state that has a dam faces no water problem. For such states the water situation is under control. - There is at least one state which has no dam. - Nothing is explicitly stated about the water situation in states without dams. - Conclusions I and II must be tested on this information only.

Concept / Approach:
The first statement is a universal conditional statement: having a dam implies no water problem. However, it does not say anything about states without dams. They might or might not have water problems. When a conclusion uses the phrase may be, it expresses that something is possible and not ruled out by the given data. If the information given allows a situation, we can often say that it may be so. Further, from a statement that links the presence of dams to the absence of water problems, we can interpret that dams are effective in solving or preventing water scarcity, which is the idea behind Conclusion II.

Step-by-Step Solution:
Step 1: From the first statement, we know that for every state with a dam, there is no water problem. So dams are associated with the removal or avoidance of water problems. Step 2: From the second statement, we know that there exists at least one state without a dam. However, nothing is specified about whether this state has a water problem or not. Step 3: Consider Conclusion I: the state without a dam may be facing a water problem. Since the premises do not guarantee the absence of water problems for states without dams, it is logically possible that such a state suffers from water scarcity. The conclusion does not claim certainty but only possibility. Therefore, this conclusion can be accepted as it is consistent with the given statements. Step 4: Now examine Conclusion II: dams solve the water problem. The first statement clearly connects having a dam with there being no water problem. This strongly supports the idea that dams are effective in solving or preventing water problems in states that have them. So Conclusion II also follows. Step 5: Together, the premises show that while states with dams do not face water issues, a state without a dam might or might not have a water problem. Hence both conclusions are compatible with the given information and follow logically.

Verification / Alternative check:
To verify, imagine two states. State A has a dam and no water problem. State B has no dam and is suffering from water shortage. This fits both statements and demonstrates Conclusion I, because the damless state is facing a problem. The same example shows that dams are associated with the absence of problems in State A, which supports Conclusion II. Since we can build such a consistent scenario and nothing in the statements contradicts it, both conclusions follow.

Why Other Options Are Wrong:
- An option that accepts only one conclusion ignores the full implications of the statements. - The option that rejects both conclusions fails to recognise that possibility based Conclusion I is not ruled out and that Conclusion II is directly supported. - The claim that the answer cannot be determined is inaccurate, because the first statement explicitly ties dams to the absence of water problems.

Common Pitfalls:
A frequent error is to assume that if dams remove water problems, then all states without dams definitely have water problems. The statements do not say this. Another mistake is to misunderstand the phrase may be as weak or unacceptable in logical reasoning. In fact, when the premises allow a situation and do not rule it out, a may be statement about that situation can be a valid conclusion.

Final Answer:
Thus, both conclusions are logically supported by the given statements, so the correct answer is Both conclusion I and conclusion II follow.