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...

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:

Extracted text: 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]