Question 2. (a) Show that there is no n EN such that n = 1 (mod 12) and n = 3 (mod 8). (b) Find a natural number n such that 3 - 1142 + 2893 = n (mod 1812). Is n unique?

Explain, with an example why the following definition, would not be suitable or useful: f(n) is Ω( g(n) ) if and only if there exists n0, such that:forall n ≥ n0, there exists c > 0 such that,f(n) ≥ c g(n)

Solve the following recurrences exactly:(a) T(1) = 8, and for all n ≥ 2, T(n) = 3T(n − 1) + 15.(b) T(1) = 1, and for all n ≥ 2, T(n) = 2T(n/2) + 6n − 1 (n is a power of 2)

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