A relation r is defined on the set z of all integers. in, Ask an Expert

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A relation R is defined on the set Z of all integers. In each case, prove that R is an equivalence relation. Find the distinct equivalence classes of R and list at least four members of each.

1- xRy if and only if x^2+y^2 is a multiple of 2.

Write x^2+y^2 as (x+y)^2-2xy

2- xRy if and only if x+3y is a multiple of 4.

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