In each of the following logical reasoning questions, a set of statements is followed by suggested conclusions. Taking the given statements to be true, even if they appear to differ from commonly known facts, read all the conclusions carefully and decide which conclusion logically follows from the given statements. Statements: (I) All insects are dangerous. (II) All machines are dangerous. Conclusions: (I) All dangerous things are insects. (II) All dangerous things are machines. (III) Some machines are insects.

Introduction / Context:
This question belongs to the standard category of syllogism based logical reasoning. You are given universal statements about insects, machines, and the property of being dangerous, and then asked to test different possible conclusions. The task is to decide which conclusion must logically follow if we accept the statements as absolutely true, even when they may not agree with real world knowledge. The focus is on set relations, not on general knowledge about insects or machines.

Given Data / Assumptions:

• Statement (I): All insects are dangerous.
• Statement (II): All machines are dangerous.
• Conclusion (I): All dangerous things are insects.
• Conclusion (II): All dangerous things are machines.
• Conclusion (III): Some machines are insects.
• We assume only the information given in the statements and do not add any extra facts.

Concept / Approach:
The problem uses the idea of sets and subsets. A statement like “All insects are dangerous” means that the set of insects is completely contained inside the set of dangerous things. In set language, insects are a subset of dangerous things. However, this does not mean that all dangerous things are insects. Similarly, “All machines are dangerous” says that machines form another subset of dangerous things. The key idea is to check whether each conclusion must be true in every possible diagram that satisfies the given statements.

Step-by-Step Solution:
Step 1: Represent insects as a subset of the set of dangerous things, based on statement (I).Step 2: Represent machines as a subset of the same set of dangerous things, based on statement (II).Step 3: Observe that the two subsets, insects and machines, may or may not overlap. There is no information that forces any machine to be an insect or any insect to be a machine.Step 4: Check conclusion (I): “All dangerous things are insects.” This would mean that the entire dangerous set is equal to the insect set. But statements only say that insects are inside dangerous, not that dangerous has nothing else. So conclusion (I) is not necessary.Step 5: Check conclusion (II): “All dangerous things are machines.” By the same reasoning, machines are inside dangerous, but dangerous can contain other things as well. So conclusion (II) is also not necessary.Step 6: Check conclusion (III): “Some machines are insects.” This requires an overlap between machines and insects. The statements do not force any such overlap, so it is possible to draw a diagram in which the two subsets do not intersect at all. Therefore this conclusion is also not guaranteed.

Verification / Alternative check:
A quick way to verify is to mentally draw a Venn diagram. Draw a large circle for dangerous things. Inside it, draw one smaller circle for insects and another separate smaller circle for machines, with no overlap. This picture satisfies both statements: every insect and every machine is dangerous. In this picture, none of the three given conclusions is true. This confirms that no conclusion logically follows from the statements.

Why Other Options Are Wrong:
Option A, claiming only conclusion (I) follows, is wrong because the statements never say that every dangerous thing is an insect. Option B, claiming only conclusion (II) follows, is wrong for the same reason with machines. Option C, claiming only conclusion (III) follows, is wrong because it is possible that machines and insects are two completely separate subsets inside the dangerous group. There is no forced overlap. Thus none of the listed conclusions must be true.

Common Pitfalls:
A very common mistake is to reverse the direction of the statements. Learners often read “All insects are dangerous” and mentally convert it into “All dangerous are insects,” which is logically incorrect. Another typical error is to assume that two different groups contained in a larger group must overlap, which is again not guaranteed. Always remember that A subset of C and B subset of C does not imply any relation between A and B. Exam questions of this type test whether you can avoid such intuitive but invalid jumps.

Final Answer:
The only logically correct decision is that no conclusion follows from the given statements.