PLEASE DO THIS BY HAND

Q4. Answer the following questions: a) Show that if d(n) is O(f(n)) and e(n) is O(g(n)), then d(n)+e(n) is O(f(n)+g(n)). b) 2n+1+n3 is O(2n): Prove or disprove COMP 352 - Winter 2023 Assignment 1 - page 1 of 2 c) Prove that 2n is O(n!) d) log(n!) is O(nlogn) : Prove or disprove e) Show that if d(n) is O(f(n)) and e(n) is O(g(n)), then d(n)e(n) is not necessarily O(f(n)g(n))