Select all the statements below which are TRUE n 1 on n2

Select all the statements below which are TRUE: n - 1 = o(n) n^2 - n + 1 = Theta (1) n^2 lg n - 10n + 100 = O(n^3) 5n^4 - 7n^2 + 10 = Theta (n^4) 2n^3 + n Squareroot n + n + 10 = omega (n^2) 2n^3 + n Squareroot n + nlgn + 10 = o(n^4)

Solution

Answerl:

n - 1 = o(n)

As per o notation f(n) < c x g(n)

Here f(n) = n - 1

g(n) = n

Now as per definition of small o :

f(n) < c x g(n)

n - 1 < c x n

f(n) is surely less than g(n) . Therefore it is true

2) 5n^4 - 7n^2 + 10 = theta(n^4)

Since the highest term in the f(n) is 5n^4 , therefore O(n^4) is True.