For each of these questions, justify your answer. Assume n n₀ for each question

(a) If I prove that an algorithm takes O(n ² ) worst-case time, is it possible that it takes O(n) on some inputs when n > n₀?

(b) If I prove that an algorithm takes O(n ² ) worst-case time, is it possible that it takes O(n) on all inputs when n > n₀?

(c) If I prove that an algorithm takes (n ² ) worst-case time, is it possible that it takes O(n) on some inputs when n > n₀?

(d) If I prove that an algorithm takes (n ² ) worst-case time, is it possible that it takes O(n) on all inputs when n > n₀?

(e) If I prove that an algorithm takes (n ² ) worst-case time, is it possible that it takes (n) on all inputs when n > n₀?