3. (14 points) In the class, we proved this theorem: If f1(n)=O(g1(n)) and f2(n)=O(g2(n)), then f1(n)+f2(n)=O(max{g1(n),g2(n)}). Prove the analogous theorems for : If f1(n)=(g1(n)) and f2(n)=(g2(n)), then f1(n)+ f2(n)=(max{g1(n),g2(n)})