Define the relation∼ on Nby m ∼ n if and only if the sum of the distinct primes that divide m is the same as the sum of the primes that divide n. For example, 12 ∼ 5 since the sum of the primes that divide 12 ( 2 + 3 ) is the same as the sum of the primes that divide 5 ( 5 ).Is ∼ an equivalence relation? Explain how you know, either providing a counterexample or briefly (not a full proof--examples are fine) explaining how you know ∼ is reflexive, symmetric, and transitive. If ∼is an equivalence relation, find a few elements of the following equivalence classes: Define the relation~on Nby m~ n if and only if the sum of the distinct primes that divide mis the same as the sum of the primes that divide n. For example, 12primes that divide 12 (2+3) is the same as the sum of the primes that divide 5 (5).5 since the sum of theIsan equivalence relation? Explain how you know, either providing a counterexample orbriefly (not a full proof--examples are fine) explaining how you know~is reflexive, symmetric,and transitive. If ~is an equivalence relation, find a few elements of the following equivalenceclasses: [0, [1], [7], [15]

To test if the given relation satisfies the conditions for reflexivity, symmetry and transitivity

Define the relation~on Nby m~ n if and only if the sum of the distinct primes that divide m is the same as the sum of the primes that divide n. For example, 12 primes that divide 12 (2+3) is the same as the sum of the primes that divide 5 (5). 5 since the sum of the Isan equivalence relation? Explain how you know, either providing a counterexample or briefly (not a full proof--examples are fine) explaining how you know~is reflexive, symmetric, and transitive. If ~is an equivalence relation, find a few elements of the following equivalence classes: [0, [1], [7], [15]

Define the relation~on Nby m~ n if and only if the sum of the distinct primes that divide m is the same as the sum of the primes that divide n. For example, 12 primes that divide 12 (2+3) is the same as the sum of the primes that divide 5 (5). 5 since the sum of the Isan equivalence relation? Explain how you know, either providing a counterexample or briefly (not a full proof--examples are fine) explaining how you know~is reflexive, symmetric, and transitive. If ~is an equivalence relation, find a few elements of the following equivalence classes: [0, [1], [7], [15]

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 3E: a. Let R be the equivalence relation defined on Z in Example 2, and write out the elements of the...

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