Read the following statements and conclusions: Statements: All snakes are trees. Some trees are roads. All roads are mountains. Conclusions: 1. Some mountains are snakes. 2. Some roads are snakes. 3. Some mountains are trees. Which of the above conclusions logically follow from the given statements?

Introduction / Context:
This is a multi step syllogism involving four sets: snakes, trees, roads and mountains. You are given three statements linking these sets and three candidate conclusions. The task is to decide which conclusions definitely follow in all possible diagrams that satisfy the given statements.

Given Data / Assumptions:

• Statement 1: All snakes are trees. (Snakes ⊆ Trees.)

• Statement 2: Some trees are roads. (There is a non empty intersection between Trees and Roads.)

• Statement 3: All roads are mountains. (Roads ⊆ Mountains.)

• Conclusion 1: Some mountains are snakes.

• Conclusion 2: Some roads are snakes.

• Conclusion 3: Some mountains are trees.

Concept / Approach:
We use Venn diagram style thinking and the rules of subset and intersection. When we have "All A are B" and "Some B are C", we know there is overlap between B and C, but not necessarily between A and C unless A is known to intersect the specific overlapping part. We must be careful not to assume more overlap than given.

Step-by-Step Solution:
Step 1: From Statement 2 and Statement 3: Some trees are roads, and all roads are mountains. Therefore, those roads that are also trees are certainly mountains. This gives "Some mountains are trees", which is Conclusion 3. Step 2: Thus, Conclusion 3 definitely follows from the combined information of Statements 2 and 3. Step 3: Check Conclusion 2: "Some roads are snakes." We know that some trees are roads, and all snakes are trees, but we are never told that any of the particular trees that are roads are snakes. It is possible that all snakes lie in a part of the Trees set that does not overlap with Roads. In such a diagram, no road would be a snake, and Conclusion 2 would be false while all statements remain true. Hence Conclusion 2 does not necessarily follow. Step 4: Check Conclusion 1: "Some mountains are snakes." All roads are mountains, and we know nothing about snakes being roads. As argued in Step 3, snakes might occupy a portion of Trees completely disjoint from Roads. Since only roads are guaranteed to be mountains, and we have no guarantee that any snake is a road, it is possible that no snake is a mountain. So Conclusion 1 does not necessarily follow.

Verification / Alternative check:
Construct a concrete diagram. Let Trees contain three distinct regions: one overlapping with Roads, one overlapping with Snakes, and one separate from both. Place all Roads entirely inside Mountains, as required. It is possible to draw the Snakes subset inside Trees but away from Roads. In this picture: • Some trees are roads (true), • All roads are mountains (true), • All snakes are trees (true), but no road is a snake and no mountain is a snake. Yet some mountains are trees via the Roads subset. This shows that only Conclusion 3 must always hold.

Why Other Options Are Wrong:
Option A and Option B focus on Conclusions 1 or 2 individually, but we have seen that neither is forced in every possible diagram. Option D claims that both 1 and 2 follow, which is even stronger and clearly incorrect. Only Conclusion 3 is guaranteed by the premises.

Common Pitfalls:
Students often assume that if A is a subset of B and B overlaps with C, then A must also overlap with C, which is not necessarily true. Overlaps can occur in different parts of the larger set. Always consider the possibility that subsets can be placed in non overlapping regions while still satisfying the given statements.

Final Answer:
The only conclusion that always follows is that some mountains are trees, so only Conclusion 3 is valid.