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Define the relation S on RxR by (x,y)S(a,b) if and only if x^2 + y^2= a^2...

Define the relation S on RxR by (x,y)S(a,b) if and only if x^2 + y^2= a^2 + b^2.

a) Prove S in an equivalence relation

b) compute [(0,0)], [(1,2)], and [(-3,4)].

c) Draw a picture in R^2 representing these three equivalence classes.

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