SOLUTION: Let S be the relation on N such that xSy means xy is not prime. Is S an equivalence relation? If yes, write down all numbers no greater than 10 from one of its equiavalence classes

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Question 1033750: Let S be the relation on N such that xSy means xy is not prime. Is S an equivalence relation? If yes, write down all numbers no greater than 10 from one of its equiavalence classes.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
S is not an equivalence relation because it fails to satisfy transitivity.

E.g. let x = 5, y = 10, z = 1. Then xSy and ySz (since 50 and 10 are not prime), but it is not true that xSz.