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Question

Which of the following is an equivalence relation on the set of all functions from Z to Z?

a.

{ (f, g) | f(x)−g(x)=1 ∀x e Z }

b.

{ (f, g) | f(0)=g(0) or f (1)=g(1) }

c.

{ (f, g) | f(0)=g(1) and f (1)=g(0) }

d.

{ (f, g) | f(x)−g(x)=k for some k ∈ Z }

Answer: (d). { (f, g) | f(x)−g(x)=k for some k ∈ Z }

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Q. Which of the following is an equivalence relation on the set of all functions from Z to Z?

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