https://file.aiquickdraw.com/mathbot/file/17290443411657yu46z0e.jpg

The question in the image asks which traversal methods (pre-order, post-order, or neither) result in vertex **c** being visited before vertex **b**. Let's analyze this using the tree provided, which has the structure:

```
        d
       / \
      c   b
     /
    e
     \
      a
```

### Tree Traversal Explanation:

1. **Pre-order traversal**:
   - Pre-order visits nodes in the order: root → left subtree → right subtree.
   - Starting at **d**, we visit **d**, then **c**, **e**, **a**, and finally **b**.
   - In this case, **c** comes before **b**, so **pre-order traversal** qualifies.

2. **Post-order traversal**:
   - Post-order visits nodes in the order: left subtree → right subtree → root.
   - Traversing the tree, we visit **a**, **e**, **c**, **b**, and finally **d**.
   - In this case, **b** comes before **c**, so **post-order traversal** does not qualify.

### Conclusion:
- The correct answer would be **Pre-order traversal**.

Would you like more details on how these traversal methods work? Here are some related questions for further understanding:

1. How is in-order traversal different from pre-order and post-order traversal?
2. Can you explain how tree traversal works for binary search trees (BSTs)?
3. What are some real-world applications of tree traversal?
4. How does depth-first search (DFS) relate to pre-order and post-order traversal?
5. How would a breadth-first traversal (BFS) behave for this tree?

**Tip**: When analyzing traversal orders, always pay attention to whether the root or the subtrees are visited first!

Select all traversals in which vertex c comes before vertex b.

Analyze tree traversal methods to determine if vertex c comes before vertex b. Learn about pre-order and post-order traversal in trees. Suitable for advanced high school students studying discrete mathematics.

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