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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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.

Akash Girde 7th Nov, 2020

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Anuj More 7th Nov, 2020

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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