Prove that the following relations are equivalenece relations and identify
equivalence classes:
1. On R, x y, if x y is an integer.
2. On R
2
,(x1, y1) (x2, y2) if x1 = x2.
3. On R
2 {(0, 0)},(x1, y1) (x2, y2) if there exists a R, a 6= 0, such that x1 = ax2
and y1 = ay2.

Question

Prove that the following relations are equivalenece relations and identify
equivalence classes:
1. On R, x  y, if x  y is an integer.
2. On R
2
,(x1, y1)  (x2, y2) if x1 = x2.
3. On R
2  {(0, 0)},(x1, y1)  (x2, y2) if there exists a  R, a 6= 0, such that x1 = ax2
and y1 = ay2.

Anuj More · Accepted Answer

Dear Akash,

What you are asking is to prove a mathematical statement. Kindly note this is not possible on this platform as we are limited by our answering ways. You may search this query on internet and you may find various portals which may help you understand your query.

Hope this helps. Thanks.

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Prove that the following relations are equivalenece relations and identify equivalence classes: 1. On R, x y, if x y is an integer. 2. On R 2 ,(x1, y1) (x2, y2) if x1 = x2. 3. On R 2 {(0, 0)},(x1, y1) (x2, y2) if there exists a R, a 6= 0, such that x1 = ax2 and y1 = ay2.

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