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On set R2 define ∼ by writing(a,b)∼(u,v)⇔ 2a−b = 2u−v. Prove that∼is an equivalence relation on...

On set R2 define ∼ by writing(a,b)∼(u,v)⇔ 2a−b = 2u−v. Prove that∼is an equivalence relation on R2

In the previous problem:

(1) Describe [(1,1)]∼. (That is formulate a statement P(x,y) such that [(1,1)]∼ = {(x,y) ∈ R2 | P(x,y)}.)

(2) Describe [(a, b)]∼ for any given point (a, b).

(3) Plot sets [(1,1)]∼ and [(0,0)]∼ in R2.

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