Problem 1: (24 points) For each pair of A and B in the list below, indicate their asymptotic relation (O,,). No justification is needed. (Assume that k1,c>1 are constants.) 1. A=nk,B=cn; 2. A=n0.1,B=2((log2n)10); 3. A=n,B=nsinn; 4. A=lg(n!),B=lg(nn). (Hint: It is possible that none or more than one of O, and relations hold for a pair of A and B.)