Discrete mathematic

question 1, 2, 3, 4

Problem 1 (4 pts): Determine whether n3=O(g(n)), where (a) g(n)=n2 (b) g(n)=n2+n3 (c) g(n)=n3log2n (d) g(n)=log2nn3. Explain your answers. Problem 2 ( 2 pts - one point of the two is bonus): Use methods discussed in class to derive tight (of the same order of growth) lower and upper bounds for i=1nlog2ii In your solution, you may use the property that for every i3,log2iilog2i+1i+1. Problem 3 (2 pts). Suppose that f(n)=O(g(n)). Does it follow that (a) 2f(n)=O(2g(n)) (b) f(n)g(n)=O(g2(n)) ? Explain your answers. Problem 4 (3pts): Show the following statements are true (a) log2(n2+n)=(log2(n)) (b) n2+nlog2n10=(n2) (c) (n+1)2n+1=(n2n)