x as nx import matplotlib.pyplot as plt

Define the set A and relation R

A = {1, 2, 3, 4} R = [(1, 1), (2, 2), (2, 3), (4, 3), (3, 4)]

Create a directed graph

G = nx.DiGraph()

Add nodes and edges

G.add_nodes_from(A) G.add_edges_from(R)

Draw the graph

plt.figure(figsize=(8, 6)) pos = nx.circular_layout(G) # Arrange nodes in a circular layout nx.draw( G, pos, with_labels=True, node_color='lightblue', node_size=2000, font_size=14, font_weight='bold', arrowsize=20 ) plt.title("Diagraph of Relation R on Set A", fontsize=16) plt.showThe diagraph of the relation $R = \{(1,1), (2,2), (2,3), (4,3), (3,4)\}$ on the set $A = \{1, 2, 3, 4\}$ is displayed. The nodes represent elements of set $A$, and directed edges depict the ordered pairs in $R$.

Would you like an explanation of the properties of this relation or have any questions?

Here are 5 related questions:

1. Is this relation reflexive, symmetric, or transitive?
2. How does the structure change if a new pair, such as $(3, 3)$, is added to $R$?
3. Can you determine if this is a partial order relation?
4. How do circular layouts help in visualizing directed graphs compared to grid layouts?
5. How would the graph look if $A$ had additional elements, e.g., $\{5, 6\}$, without any edges?

Tip: Always check properties like reflexivity, symmetry, and transitivity to better understand a relation.