SOLUTION: Let S be the relation on N such that xSy means xy is a perfect square. Show that S is an equivalence relations. Write down all numbers no greater than 30 from one of its equiavalen

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Question 1027829: Let S be the relation on N such that xSy means xy is a perfect square. Show that S is an equivalence relations. Write down all numbers no greater than 30 from one of its equiavalence classes
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
1. S is reflexive: It is obvious that xSx is true.
2. S is symmetric: xSy true implies that ySx is also true, because xy = ys is a perfect square.
3. S is symmetric.
xSy ==> xy = k%5E2 for some integer k ==> x+=+k%5E2%2Fy is an integer.
ySz ==> yz = l%5E2 for some integer l ==> z+=+l%5E2%2Fy is an integer.
==> xz is an integer that is a perfect square, since, xz+=+%28k%5E2%2Fy%29%28l%5E2%2Fy%29+=+%28%28kl%29%2Fy%29%5E2
Therefore S is an equivalence relation.
E.g., [16] = {(16,1), (8,2), (4,4), (2,8), (1,16)}