For each of the following problems, determine whether the given statement is true. If yes, provide a proof; otherwise, just answer no. Problem 1. 5n + 3 n = O(2n + 2). Problem 2. 5n + 3 n = O(n). Problem 3. n 2 = O(1000 n log n). Problem 4. n log2 n = O( n). Problem 5. If functions f(n) = O(n log n) and g(n) = O( n), then f(n) + g(n) = O(n log n). Problem 6. If functions f(n) = O(n log n) and g(n) = O( n), then f(n) + g(n) = (n log n). Problem 7. If functions f(n) = (n log n) and g(n) = ( n), then f(n) + g(n) = (n log n)

For each of the following problems, determine whether the given statement is true. If "yes", provide a proof; otherwise, just answer "no". Problem 1. 5n+3n=O(2n+2). Problem 2. 5n+3n=O(n). Problem 3. n2=O(1000nlogn). Problem 4. log2nn=O(n). Problem 5. If functions f(n)=O(nlogn) and g(n)=O(n), then f(n)+g(n)=O(nlogn). Problem 6. If functions f(n)=O(nlogn) and g(n)=O(n), then f(n)+g(n)=(nlogn). Problem 7. If functions f(n)=(nlogn) and g(n)=(n), then f(n)+g(n)=(nlogn)