Question

Determine if the following statements are true or false.

In either case, provide a formal proof using the definitions of the big-O, big-Omega, and big-Theta notations. For instance, to formally prove that f (n) ∈ O(g(n)) or f (n) ∉ O(g(n)), we need to demonstrate the existence of a constant c and a sufficient large n0 such that f (n) ≤ c g(n) for all n ≥ n0, or showing that there are no such values.

a) [1 mark] 10000n2 ∈ O(n4).

b) [1 mark*] 2nn2 ∈ Ω(3n).
c) [1 mark] 3n2 + 4n ∈ Θ(n).

Could i please ask to see hand written working if possible?? Helps me understands better ! Thanks

Answer 1

In case of any queries, please revert back.

I have hand written for you. Please upvote if this helps.