I see that the file contains questions related to discrete mathematics. I'll solve the provided problems and explain step-by-step. Here's the analysis and solution to each question.

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Question 1: Graph Representation

Given:

• $V = \{1, 2, 3, 4, 5\}$
• $E = \{\{1, 2\}, \{1, 5\}, \{2, 3\}, \{2, 4\}, \{3, 4\}, \{4, 5\}\}$

Solution Steps:

1. Vertices: List the vertices in the graph. $V = \{1, 2, 3, 4, 5\}$.
2. Edges: Represent each edge in the set $E$ as connections between vertices.
3. Graph: Draw the graph $G = (V, E)$ with each edge connecting its corresponding vertices.

Graph Sketch:

• Nodes: $1, 2, 3, 4, 5$
• Connections:
  • $1 \leftrightarrow 2$
  • $1 \leftrightarrow 5$
  • $2 \leftrightarrow 3$
  • $2 \leftrightarrow 4$
  • $3 \leftrightarrow 4$
  • $4 \leftrightarrow 5$

I'll prepare a drawing if needed for clarity.

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Question 2(a)(i): Walk of Length 4

A walk is any sequence of vertices where consecutive vertices are connected by edges.

Steps:

1. Select starting vertex: For example, $1$.
2. Create sequence of length 4: Ensure each consecutive pair is connected by an edge.

One possible walk: $1 \to 2 \to 3 \to 4 \to 5$.

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Question 2(a)(ii): Path of Length 3 from $V_1$ to $V_4$

A path is a walk with no repeated vertices.

Steps:

1. Start at $V_1 = 1$.
2. End at $V_4 = 4$.
3. Choose intermediate vertices ensuring no repetition.

One valid path: $1 \to 2 \to 3 \to 4$.

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Question 2(b): Additional Details

This portion appears truncated or unclear in the uploaded file. If you clarify, I'll solve it accordingly.

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Would you like a visual representation of the graph or further clarification? Let me know!