Exercise I (15 points) Consider two algorithms A, and A2 that have the running times Ti(n) and T2(n), respectively. Ti(n) = T, (n) = 100n + 100n and T; (n) = 0.1n + 0.1n a) (12 points) Use the definition of 0) to show that Ti(n) E O(T2(n)). b) (3 points) Which algorithm should you use? A, or A2? Justify Exercise 2 (15 points) Consider two algorithms A, and A2 that have the running times Ti(n) and T2(n), respectively. Ti(n) = T, (n) = 100n? + 100n and T; (n) = 0.1n? + 0.1n a) (12 points) Use the definition of 0) to show that Ti(n) E N(T2(n)). b) (3 points) Show that Ti(n) E O(T2(n))