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We define a relation on the integers as follows: For all integers , ∈ Z, if and only if 5|( − ).

  1. How do I prove that is an equivalence relation.
  2. How do I give a description of the equivalence class [2] and find at least 3 members of this equivalence class?
leo
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  • As a further push in understanding this problem... you should be very familiar with the equivalence relation where it was instead $xRy$ if and only if $10\mid (x-y)$. That equivalence relation is more commonly described as "Ending in the same digit" – JMoravitz Oct 14 '19 at 18:14