Question: In this Lab, N = {1, 2, 3, ...} Exercise 1. Let f be a function from N to N with f(n) = n 2

In this Lab, N = {1, 2, 3, ...}

Exercise 1. Let f be a function from N to N with f(n) = n 2 + n + 1

a) Show that f injective (one-to-one).

b) Is f surjective (onto)?

Exercise 2. let R be the binary relation defined by : xRy iff x 2 ? y 2 is divisible by 3 where x, y ? Z. Is R an equivalence relation(Reflexive, Symmetric and Transitive)?

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