In the following question, some statements and conclusions based on them are given. Read the statements carefully and, assuming them to be true, decide which of the given conclusions logically follows. Statements: I. All rackets are bats. II. All bats are wickets. Conclusions: I. Some wickets are rackets. II. All wickets are rackets.

Introduction / Context:
This is a classic syllogism question often seen in logical reasoning sections of competitive exams. You are given two statements, also called premises, and two possible conclusions. Your job is to assume that the statements are absolutely true, even if they seem strange in real life, and then determine which conclusion or conclusions must logically follow from those statements.

Given Data / Assumptions:
- Statement I: All rackets are bats. - Statement II: All bats are wickets. - Conclusion I: Some wickets are rackets. - Conclusion II: All wickets are rackets. - We must accept the statements as true and judge the conclusions only on logical structure.

Concept / Approach:
Syllogism problems usually involve set relations such as all, some and no. From All A are B and All B are C, we can infer that All A are C. However, we cannot automatically claim anything about all of C from A. Here, we can symbolise rackets as R, bats as B and wickets as W. Statement I says all R are B. Statement II says all B are W. From this we get all R are W. Once we know that, we can check which conclusions are guaranteed to be true: that some W are R and that all W are R.

Step-by-Step Solution:
Step 1: Draw the basic relation in mind. All rackets are inside the set of bats, and the set of bats lies inside the set of wickets. Step 2: From this nesting, it follows that every racket is also a wicket, because every racket is a bat and every bat is a wicket. Step 3: If all rackets are wickets, and there is at least one racket in the universe of discourse, then there is at least one object that is both a racket and a wicket. Therefore, some wickets are rackets is logically true and conclusion I follows. Step 4: Check conclusion II, which states that all wickets are rackets. This would mean that the set of wickets is fully inside the set of rackets, but the statements never say that. They only say that rackets go into bats and bats into wickets, not that all wickets come back into rackets. Step 5: It is possible that there are many wickets that are not bats and therefore not rackets. Since a possible diagram exists where some wickets are not rackets, conclusion II does not follow with necessity.

Verification / Alternative check:
Consider a simple example. Suppose there are 10 rackets, all of which are bats, and all those bats are wickets. In addition, there are 90 more wickets that are neither bats nor rackets. In this situation, statement I and statement II are both true. Conclusion I is true because some of the wickets, namely the 10 that are also rackets, are indeed rackets. However, conclusion II, which claims that all wickets are rackets, is clearly false because the extra 90 wickets are not rackets. Since we have found a case where the statements are true but conclusion II is false, conclusion II does not logically follow.

Why Other Options Are Wrong:
Option B is wrong because conclusion II alone does not follow, as explained above. Option C is wrong because conclusion I definitely follows from the given statements. Option D is wrong because it claims that both conclusions follow, but conclusion II fails in some possible cases.

Common Pitfalls:
A common mistake is to confuse the direction of statements and assume that if all rackets are bats and all bats are wickets, then all wickets must be rackets. This is the fallacy of taking the converse of a statement. Another pitfall is ignoring the possibility of extra elements in the larger set of wickets. Good practice when solving syllogism questions is to draw simple Venn diagrams or imagine nested sets, and to test whether a conclusion must always be true or can fail in at least one possible arrangement.

Final Answer:
Only conclusion I follows, so the correct option is “Only conclusion I follows.”