https://file.aiquickdraw.com/mathbot/file/1726839053412ai8wgrvp.jpg

Let's analyze the problem in the image:

### The diagram shows a graph with 5 vertices \( P, Q, R, S, T \) and a set of edges. The problem asks which of the following statements is true about the graph.

### Statements:

- **A:** This graph is a directed graph.
- **B:** The degree of vertex \( Q \) is 2.
- **C:** The sum of the degrees of the graph is 12.
- **D:** Set \( E = \{P, Q, R, S, T\} \) and \( V = \{(P, Q), (P, T), (Q, R), (T, S)\} \).

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### Step 1: Analyze the type of graph.
From the diagram, there are no arrows on the edges, so the graph is undirected.  
- **A is false.**

### Step 2: Check the degree of vertex \( Q \).
- \( Q \) is connected to both \( P \) and \( R \), giving it two edges.  
- **B is true.**

### Step 3: Calculate the sum of the degrees of the graph.
- Degree of \( P = 2 \) (connected to \( Q \) and \( T \)).
- Degree of \( Q = 2 \) (connected to \( P \) and \( R \)).
- Degree of \( R = 2 \) (connected to \( Q \) and \( S \)).
- Degree of \( S = 2 \) (connected to \( R \) and \( T \)).
- Degree of \( T = 2 \) (connected to \( P \) and \( S \)).

Thus, the sum of the degrees is \( 2 + 2 + 2 + 2 + 2 = 10 \).  
- **C is false.**

### Step 4: Verify the set notation in \( D \).
- Set \( E \) represents the vertices \( \{P, Q, R, S, T\} \), which is correct.
- Set \( V \) represents the edges: \( (P, Q), (P, T), (Q, R), (T, S) \), which is also correct as it matches the edges in the diagram.

So, **D is true**.

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### Conclusion:
- The correct answers are **B** and **D**.

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Would you like further details or have any questions?  
Here are 5 related questions for deeper understanding:

1. What is the difference between directed and undirected graphs?
2. How do you compute the degree of a vertex in a graph?
3. What is the significance of the sum of degrees in a graph?
4. How does graph theory apply in real-world scenarios?
5. How can you represent a graph using an adjacency matrix or list?

#### Tip: The sum of the degrees of a graph is always twice the number of edges in an undirected graph!

Which of the following statements is true about the graph?

This problem asks you to analyze a graph and determine the truth of various statements regarding vertex degrees, the sum of degrees, and graph type. Learn how to apply key graph theory concepts like undirected graphs and the degree of a vertex, suitable for students in Grades 10-12.

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