State whether the statements are correct or incorrect with reasons.1. O(f(n)) + O(f(n)) = O (2f(n))2. If 3n + 5 = O(n2) , then 3n + 5 = o(n2)

1. O(f(n)) + O(f(n)) = O(2f(n)) - Correct

Explanation: In Big O notation, when we add two functions, the dominant term is the one that determines the overall complexity. Since both O(f(n)) and O(f(n)) have the same function f(n), adding them together will still result in the same dominant term. Therefore, O(f(n)) + O(f(n)) is equivalent to O(2f(n)).

2. If 3n + 5 = O(n^2), then 3n + 5 = o(n^2) - Incorrect

Explanation: In Big O notation, the symbol "O" represents an upper bound, while the symbol "o" represents a strict upper bound. If 3n + 5 is O(n^2), it means that there exists a constant c and a value n0 such that for all n ≥ n0, 3n + 5 ≤ c * n^2. However, this does not imply that 3n + 5 is strictly less than c * n^2 for all n ≥ n0. Therefore, we cannot conclude that 3n + 5 is o(n^2).