https://file.aiquickdraw.com/mathbot/file/1729371130835uafcgqsu.jpg

Here is the directed graph for the relation \( R \). Each directed edge represents a pair \( (a, b) \) from the relation, with loops for reflexive pairs (like \( (1, 1) \), \( (2, 2) \), etc.).

Would you like more details on how to interpret this graph, or have any other questions about it?

Here are five follow-up questions for deeper understanding:
1. How can you verify if the graph reflects the reflexive property of the relation?
2. Can you identify which edges show symmetry in this graph?
3. How would you check for transitivity in this directed graph?
4. What does the presence of loops (like \( 1 \to 1 \)) indicate about the relation?
5. How can you use this graph to identify equivalence classes for \( S / R \)?

**Tip**: When drawing directed graphs, loops indicate that the element relates to itself, which is a key feature of reflexive relations.

Create the directed graph of R and show that R is an equivalence relation by proving it satisfies reflexivity, symmetry, and transitivity.

Learn how to create the directed graph of a relation R on a set S and prove that R is an equivalence relation. This includes proving reflexivity, symmetry, and transitivity, with step-by-step explanations.

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