https://file.aiquickdraw.com/mathbot/file/1730246050478p1eyove4.jpg

To solve this problem, we need to interpret the directed graph, which represents the relation \( W \), and then determine \( W \rightarrow (4) \).

1. **Understanding \( W \rightarrow (4) \)**:
   - \( W \rightarrow (4) \) represents the set of elements that have a direct path (directed edge) to node 4. We need to identify the nodes with edges pointing to 4 in the graph.

2. **Analyzing the Graph**:
   - Looking at the graph, let's find all nodes connected to node 4:
     - Node 1 has a directed edge going to node 4.
     - Node 3 also has a directed edge going to node 4.
   - So, the elements that map directly to 4 are **1 and 3**.

3. **Identifying \( W \rightarrow (4) \)**:
   - Since nodes 1 and 3 have directed edges pointing to node 4, \( W \rightarrow (4) \) should include 1, 3, and 4.

4. **Choosing the Correct Answer**:
   - Among the choices, the answer that includes {1, 3, 4} is:
     - **Option C: {1, 3, 4}**

Thus, the correct answer is **Option C: {1, 3, 4}**.

Would you like further details on graph theory concepts or how to interpret directed graphs in relation problems?

### Related Questions:
1. What does it mean if there is a cycle in a directed graph?
2. How would you find all elements in a relation that lead to multiple nodes?
3. Can we use matrix representation to analyze relations in directed graphs?
4. How do we interpret transitive relations in directed graphs?
5. What are the characteristics of reflexive relations in graph representation?

**Tip:** In directed graphs, always check the direction of the arrows carefully to understand which elements are related in a given relation.

Let the relation W be represented by the directed graph below. What is W→(4)?

Discover how to interpret a directed graph to solve for W→(4) in relation W. This problem involves understanding directed edges to determine which nodes map to node 4. Ideal for college-level students studying graph theory and relations.

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