Problem 1. This is basically Problem 3.2-3 (pg 62) in CLRS textbook. For each of the two statements below, show that it's either true or false. The statements have the form: is f(n)=O(g(n)). To show it's true, find constants c and M such that for all nM,f(n)cg(n). To show it's false, show for any constant c, there is no constant M such that nM,f(n) cog(n). (a) [1pt] Is 2n+1=O(2n)? (b) [1pt] Is 22n=O(2n)? Problem 2. This comes from Problem 3-4 (pg 72) in CLRS textbook. Let f(n) and g(n) be asymptotically positive functions. Prove or disprove each of the following conjectures. Hint: to disprove, you can choose an appropriate f(n) and/or g(n). (a) [1pt]f(n)=O(g(n)) implies 2f(n)=O(2g(n)) (b) [1 pt ]f(n)=(f(2n))