Big O notation true or false questions Are these true or fal

Big O notation true or false questions?

Are these true or false? Using true (not abused) meaning of Big-O (and Big-Omega), not just the tightest bound

Answer:

6. n^2 + logn^2 = omega (n)

It is true , check f(n) > = c1*g(n)

here f(n) = n^2 + logn^2 = n^2 + nlong , g(n) = n

now omega definition : f(n) > = c1*g(n)

= n^2 + nlogn > = n * c1

It satisfies the definition by c = 1 and n = 2

thus it is true

7. True , as n^n is always greater than n!

8. It is true as in the given equation logn is the highest term.

9. It is false as it is dependent on n so cannot take constant time.

10. It is true as the highest term in the equation is n^6.