Math Problem Statement

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)}

Solution

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

  1. Find the cross product A×AA \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×AA \times A

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

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

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Math Problem Analysis

Mathematical Concepts

Set Theory
Relations

Formulas

-

Theorems

Equivalence Relation Theorem

Suitable Grade Level

College Level

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