In this statement and conclusion type question, you are given three statements about cups, plates, spoons, and the colour blue. Accept the statements as true even if they appear unrealistic, read all the conclusions carefully, and then decide which conclusions logically follow. Statements: (I) Some cups are plates. (II) All spoons are blue. (III) No plates are spoon. Conclusions: (I) Some cups are not spoon. (II) Some plates are not blue. (III) Some cups are not blue. (IV) Some blue are not plates.

Introduction / Context:
This question explores a slightly more complex web of relations involving cups, plates, spoons, and blue objects. You are given three statements and four candidate conclusions, and you must carefully evaluate each conclusion. The problem tests your ability to combine several set relations and to handle both “some” and “no” statements at the same time.

Given Data / Assumptions:

• Statement (I): Some cups are plates.
• Statement (II): All spoons are blue.
• Statement (III): No plates are spoon.
• Conclusion (I): Some cups are not spoon.
• Conclusion (II): Some plates are not blue.
• Conclusion (III): Some cups are not blue.
• Conclusion (IV): Some blue are not plates.
• We accept the conventional exam assumption that when a universal statement like “All spoons are blue” is discussed in this context, spoons exist.

Concept / Approach:
The key ideas are: some cups are plates, no plate is a spoon, and all spoons are blue. From these, we can deduce information about cups that are plates and about blue objects that come from the spoons group. For each conclusion, we should either derive it directly or construct a counterexample that satisfies all statements but makes the conclusion false. Conclusions that survive this scrutiny are the ones that logically follow.

Step-by-Step Solution:
Step 1: From statement (I), there exists at least one object that is both a cup and a plate.Step 2: From statement (III), no plate is a spoon. Therefore, any object that is a plate cannot be a spoon.Step 3: Combine steps 1 and 2. The object that is both a cup and a plate is not a spoon, because all plates are not spoons. Hence at least one cup is not a spoon. This directly supports conclusion (I): “Some cups are not spoon.”Step 4: Examine conclusion (II): “Some plates are not blue.” We know only that no plate is a spoon and all spoons are blue. Plates could still be blue items that are not spoons. The statements do not say that plates are never blue. It is possible that every plate is blue but none is a spoon. Therefore we cannot guarantee that some plates are not blue, so conclusion (II) does not necessarily follow.Step 5: Examine conclusion (III): “Some cups are not blue.” Again, nothing in the statements restricts cups from being blue or not blue. Some cups that are plates might be blue or not blue, and cups that are not plates are completely unconstrained by the statements. It is possible that, in one valid scenario, every cup is blue. Since we can construct such a case, conclusion (III) does not logically follow.Step 6: Examine conclusion (IV): “Some blue are not plates.” From statement (II), all spoons are blue, and from statement (III), no plate is a spoon. This implies that spoons are blue objects that cannot be plates. Under the usual exam assumption that spoons actually exist, at least one spoon exists, which is blue and not a plate. Hence there is at least one blue object that is not a plate. Conclusion (IV) therefore follows.

Verification / Alternative check:
We can verify with a concrete model. Suppose there is one object that is both a cup and a plate, and that object is blue. Also suppose there is at least one spoon that is blue and not a plate. Further, let all plates be blue, and let all remaining cups be blue as well. In this model, all three statements hold: some cups are plates, all spoons are blue, and no plates are spoons. Check the conclusions: there is a cup that is a plate and not a spoon, so conclusion (I) holds. There is no plate that is not blue, so conclusion (II) fails. There is no cup that is not blue, so conclusion (III) fails. There is at least one spoon that is blue and not a plate, so conclusion (IV) holds. Thus only conclusions (I) and (IV) are forced by the statements.

Why Other Options Are Wrong:
Option A includes conclusion (III), but we have shown that it can be false in a valid arrangement. Option B and option C both include conclusion (II), which is not compelled because plates may all be blue. Option D, which claims that only conclusions (I) and (IV) follow, matches the analysis. There is no option that lists just conclusion (I), so we must rely on the careful reasoning that shows (IV) is also valid.

Common Pitfalls:
One common mistake is to assume that if all spoons are blue, then blue objects must be spoons, which reverses the logic. Another typical error is to think that if some cups are plates and no plates are spoons, then those cups are automatically not blue, which is not supported by the statements. Always distinguish between being restricted from being a spoon and being restricted from being blue, as they are different properties here.

Final Answer:
Hence, the correct decision is that only conclusions (I) and (IV) follow from the given statements.