1. (20 points). For each of the following claims, decide if it is true or false. No explanation is needed. (a) (2 points) n log n = O(n). (b) (2 points) log log n = O(log n). (c) (2 points) log50 n = = O(n0.1). (d) (2 points) 4" = 0(2"). (e) (2 points) 100100 = (1). (f) (2 points) if f = 0(9), then g=12(f). (g) (2 points) if n3 = 2(n). (h) (2 points) If an algorithm's worst case running time is O(n), it means that the running time is O(n?) for all inputs of size n. (i) (2 points) 100 + 200n + 300n2 = O(n?) (j) (2 points) 21= log i = O(n log n)