Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.