In this statement and conclusion question, you are given two statements about graduates, men, and a thief. You must treat the statements as true and decide which conclusions I and II logically follow. Statement I: A graduate is a man. Statement II: This thief is a graduate. Conclusion I: This thief is a man. Conclusion II: Some men are thieves.

Introduction / Context:
This question combines a general statement about graduates and men with a specific statement about a person described as a thief. The task is to work out whether the thief must be a man and whether this implies that some men are thieves. It is a straightforward application of set inclusion and existence reasoning.

Given Data / Assumptions:
- Statement I: A graduate is a man, which means every graduate belongs to the set of men.
- Statement II: This thief is a graduate, which means the specific person under discussion belongs to the set of graduates.
- Conclusion I: This thief is a man, asserting that the specific thief belongs to the set of men.
- Conclusion II: Some men are thieves, asserting that the intersection of the sets men and thieves is non empty.

Concept / Approach:
Let G represent the set of graduates, M the set of men, and T the set of thieves. From Statement I, G ⊆ M. From Statement II, the specific thief, call this person x, is in G. When an element belongs to a subset, it also belongs to the corresponding superset. This lets us infer that x is in M. Once we know x is both a man and a thief, we can infer the existence of at least one man who is a thief, which supports the second conclusion.

Step-by-Step Solution:
Step 1: From Statement I, every graduate is a man. Symbolically, if y ∈ G then y ∈ M. Step 2: From Statement II, the specific thief x is a graduate, so x ∈ G. Step 3: Combining these facts, x ∈ G implies x ∈ M. Therefore, the thief is also a man, which supports Conclusion I. Step 4: We also know that x is both a thief and a man; x belongs to T and M simultaneously. Step 5: This means the intersection M ∩ T is non empty, because it contains at least the element x. Step 6: Hence there is at least one man who is a thief. This is exactly what Conclusion II states: some men are thieves. Step 7: Therefore, both Conclusion I and Conclusion II logically follow from the two given statements.

Verification / Alternative check:
Imagine the universe of people. First mark the set of graduates and place it fully inside the set of men, reflecting Statement I. Then designate a specific individual x as a thief and also place x inside the graduates set, reflecting Statement II. The picture now shows x inside both the set of men and the set of thieves. This confirms that the thief is a man and that at least one man is a thief. Any interpretation that satisfies the original statements will always produce the same logical consequence.

Why Other Options Are Wrong:
Option A chooses only Conclusion I, ignoring the fact that the existence of a man who is a thief also proves Conclusion II. Option B chooses only Conclusion II, but it misses the straightforward consequence that the specific thief is a man. Option C says neither follows, which is inconsistent with the clear logical chain from the statements. Option E suggests that exactly one of the conclusions must be true, which is also wrong since both are true in every valid interpretation.

Common Pitfalls:
A typical error is to assume that when we talk about "some men are thieves," we need a large group or multiple examples. In logic, "some" means at least one. As soon as you have identified a single individual who belongs to both sets, the statement "some men are thieves" becomes true. Another mistake is to treat the phrase "this thief" as if it could somehow be outside the set of graduates despite Statement II explicitly including the thief in that set.

Final Answer:
The correct option is Both I and II follows, because the thief, being a graduate, must be a man, and this guarantees that at least one man is a thief.