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}š¯‘…1 = {(4, 2), (4, 6), (6,2)}

š¯‘…2 = {(2,2), (2,4), (4,2), (4,4), (6,6)}

š¯‘…3 = {(2,4), (4,4), (6,4)}

Solution

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

  1. Find the cross product AĆ—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 AĆ—AA \times A

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

The cross product AĆ—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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