Find the cross product then determine whether the following is a: Relation, Reflexive, Irreflexive, Transitive, Symmetric, Antisymmetric and Equivalence Relation.

1. A = {2, 4, 6}𝑅1 = {(4, 2), (4, 6), (6,2)}

𝑅2 = {(2,2), (2,4), (4,2), (4,4), (6,6)}

𝑅3 = {(2,4), (4,4), (6,4)}

To tackle the problem, let's follow these steps:

1. **Find the cross product \( A \times A \)**.
2. **Analyze each relation (R1, R2, R3) to determine if it is Reflexive, Irreflexive, Transitive, Symmetric, Antisymmetric, and if it forms an Equivalence Relation**.

### 1. Cross Product \( A \times A \)

Given:
\[ A = \{2, 4, 6\} \]

The cross product \( A \times A \) is:
\[ A \times A = \{(2,2), (2,4), (

Explore the analysis of relations in set theory: Reflexive, Irreflexive, Transitive, Symmetric, and Antisymmetric properties. Understand how these properties determine the nature of relations using specific examples from set A = {2, 4, 6} and relations R1, R2, R3.

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