Hello for every one,
I have a question about real analysis Q: let S be the cartesian Coordinate plane RxR and define a relation R on S by (a,b)R(c,d) iff a+d=b+c Verify that R is an equivalence relation.
I know that i have to proof R is reflexive, Symmetric and transitive
a) Reflexive: I have to show (a,b)R(a,b) for all (a,b) belong to RxR
b) Symmetric: (a,b)R(c,d) implies (c,d)R(a,b) for all (a,b)R(c,d) belong to RxR
c) Transitive: (a,b)R(c,d) and (c,d)R(e,f) implies that (a,b)R(e.f) for all (a,b),(c,d),(e,f) belong to RxR
can any one explain to me in detail
thanks in advance
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