1. Let g(n) be a function. For each of the following statements, mark in the answer sheetswhether it is correct (true = correct, false = incorrect).(a) Θ(g) = {f (n) : There exist positive constants c1, c2 and n0 such that0 ≤ c1 · g(n) ≤ f (n) ≤ c2 · g(n), for all n ≥ n0}(b) Θ(g) = {f (n) : There exist positive constants c1, c2 and n0 such that0 ≤ c1 · f (n) ≤ g(n) ≤ c2 · f (n), for all n ≥ n0}(c) Θ(g) = O(g) ∩ Ω(g)

A) Big-O notation and loop invariants1. Let g(n) be a function. For each of the following statements, mark in the answer sheetswhether it is correct (true = correct, false = incorrect).(a) Θ(g) = {f (n) : There exist positive constants c1, c2 and n0 such that0 ≤ c1 · g(n) ≤ f (n) ≤ c2 · g(n), for all n ≥ n0}(b) Θ(g) = {f (n) : There exist positive constants c1, c2 and n0 such that0 ≤ c1 · f (n) ≤ g(n) ≤ c2 · f (n), for all n ≥ n0}(c) Θ(g) = O(g) ∩ Ω(g)

Which of the following functions is Θ(n2)?

For each of the following statements, mark in the answer sheets whether the statement istrue or false.(a) Let f and g be positive functions. Then, f (n) + g(n) ∈ O(n) implies that f ∈ O(n)and g ∈ O(n).(b) There exist functions f, g ∈ Ω(n) such that f − g ∈ Ω(g) and 2g − f ∈ Ω(f ).

Consider the given functions.Select the true statement regarding the end behavior of the functions. A. As the value of x increases, f and h both approach positive infinity. B. As the value of x increases, f and g both approach positive infinity. C. As the value of x increases, g is the only function to approach 0. D. As the value of x increases, f is the only function to approach 0.

f(n) = 2^(2n)Which of the following correctly represents the above function?Select one:O(2^n)Ω(2^n)Θ(2^n)None of these