algorithms

3. Asymptotic Notation Properties. (20 points) Let f(n) and g(n) be asymptotically non-negative functions. Using the definitions of asymptotic notation: (a) (5 points) Prove that if f(n)=o(g(n)) and g(n)=o(h(n)) then f(n)=o(h(n)). (b) (5 points) Prove that if f1(n)=O(g1(n)) and f2(n)=O(g2(n)) then f1(n)+f2(n)= O(g1(n)+g2(n)) (c) (5 points) Prove that if f(n)=O(n)+O(n2)+O(n3) then f(n)=O(n3). (d) (5 points) Disprove that if f(n)=O(g(n)) and g(n)=(h(n)) then f(n)=(h(n)). To do this, you need to provide a counterexample by showing a specific f(n),g(n),h(n) that do not satisfy the above statement