A non-negative function f: N - R is polynomially bounded, written f(n)- poly(n), if f(n)- O(n) for somc constant e20. A non-negative function e: N-R is negligihle, written e(n) negl(n), if it decreases faster than the inverse of any polynomial. Formally: lim, (n) n-0 for any constant e20. (Otherwise, we say that e(n) is non-negligible.) (a) Are following functions negligible or not? Prove your answer. (Why doesn't the base of the logarithm matter in both cases?) (n) = log(n") E2(n) (b) Suppose that ce(n)-negl(n) and f(n) - poly(n). Is it always the case that f(n)-e(n) - negl(n)? If so, prove it; otherwise, give concrete functions e(n). (n) that serve as a counterexample. A non-negative function f: N - R is polynomially bounded, written f(n)- poly(n), if f(n)- O(n) for somc constant e20. A non-negative function e: N-R is negligihle, written e(n) negl(n), if it decreases faster than the inverse of any polynomial. Formally: lim, (n) n-0 for any constant e20. (Otherwise, we say that e(n) is non-negligible.) (a) Are following functions negligible or not? Prove your answer. (Why doesn't the base of the logarithm matter in both cases?) (n) = log(n") E2(n) (b) Suppose that ce(n)-negl(n) and f(n) - poly(n). Is it always the case that f(n)-e(n) - negl(n)? If so, prove it; otherwise, give concrete functions e(n). (n) that serve as a counterexample