Draw a diagraph of relation 
𝑅
=
{
(
1
,
1
)
,
(
2
,
2
)
,
(
2
,
3
)
,
(
4
,
3
)
,
(
3
,
4
)
}
R={(1,1),(2,2),(2,3),(4,3),(3,4)} on set 
𝐴
=
{
1
,
2
,
3
,
4
}
A={1,2,3,4}.

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.

Draw a diagraph of relation R={(1,1),(2,2),(2,3),(4,3),(3,4)} on set A={1,2,3,4}.

Explore how to draw the diagraph of the relation R={(1,1),(2,2),(2,3),(4,3),(3,4)} on the set A={1,2,3,4}. This step-by-step guide visualizes the relation as a directed graph, showing nodes and edges for ordered pairs in the relation. Suitable for high school students studying set theory and relations.

Math Problem Statement

Draw a diagraph of relation 𝑅

{ ( 1 , 1 ) , ( 2 , 2 ) , ( 2 , 3 ) , ( 4 , 3 ) , ( 3 , 4 ) } R={(1,1),(2,2),(2,3),(4,3),(3,4)} on set 𝐴

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