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Let A=NxN and define a relation on A by (a,b)R(c,d) when a⋅b=c⋅d a ⋅ b =...

Let A=NxN and define a relation on A by (a,b)R(c,d) when a⋅b=c⋅d a ⋅ b = c ⋅ d . For example, (2,6)R(4,3)

a) Show that R is an equivalence relation.

b) Find an equivalence class with exactly one element.

c) Prove that for every n ≥ 2 there is an equivalence class with exactly n elements.

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