A The root of the Tree above is node F. A neighbor of node X is any node which shares an edge with X (e.g. G and I are neighbors while H and E are not). A sibling of node X is any node which shares a parent with X. An ancestor of node X is any node on the unique path from X to the root of the tree. X is a descendent of Y if Y is an ancestor of X. Assume that the sibling, neighbor, ancestor and descendent relation are reflexive while the parent and child relations are not. Express the set all the nodes which meet each of the following criteria. 1 iii Sibling of D iv Ancestor of H v Descendent of B

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Chapter2: Second-order Linear Odes
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**Tree Anatomy**

The diagram shows a binary tree with the following structure:

- The root of the tree is node F.
- Nodes are connected as follows:
  - F has children B and G.
  - B has children D and A.
  - D has children A and C.
  - G has children I and H.
  - I has child E.

**Definitions:**

- **Neighbor of node X**: Any node that shares an edge with X (e.g., G and I are neighbors while H and E are not).
- **Sibling of node X**: Any node that shares a parent with X.
- **Ancestor of node X**: Any node on the unique path from X to the root of the tree.
- **Descendent of Y**: If Y is an ancestor of X, then X is a descendant of Y.
- **Assumptions**: The sibling, neighbor, ancestor, and descendent relationships are reflexive, while the parent and child relationships are not.

**Instructions:** 

Express the set of all nodes which meet each of the following criteria:

iii. Sibling of D
iv. Ancestor of H
v. Descendent of B
vi. The set of neighbors of D or G which are not also neighbors of B.
Transcribed Image Text:**Tree Anatomy** The diagram shows a binary tree with the following structure: - The root of the tree is node F. - Nodes are connected as follows: - F has children B and G. - B has children D and A. - D has children A and C. - G has children I and H. - I has child E. **Definitions:** - **Neighbor of node X**: Any node that shares an edge with X (e.g., G and I are neighbors while H and E are not). - **Sibling of node X**: Any node that shares a parent with X. - **Ancestor of node X**: Any node on the unique path from X to the root of the tree. - **Descendent of Y**: If Y is an ancestor of X, then X is a descendant of Y. - **Assumptions**: The sibling, neighbor, ancestor, and descendent relationships are reflexive, while the parent and child relationships are not. **Instructions:** Express the set of all nodes which meet each of the following criteria: iii. Sibling of D iv. Ancestor of H v. Descendent of B vi. The set of neighbors of D or G which are not also neighbors of B.
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