Which one of the following is invalid explain n On n On n

Which one of the following is invalid, explain?

(n) + O(n) = (n)

O(n) + (n) = (n)

(n) + O(n) = O(n)

f(n) = O(g(n)) implies g(n) = (f(n))

f(n) = O(g(n)) implies g(n) = O(f(n)) It is invalid

For example, log(n) is of O(n), but n is not of O(log(n)).

And Division by O is either misunderstanding of the notation.

Sequences or functions that are f(n)/g(n) remains bounded, but g(n)/f(n) doesn\'t.

So, In the \"big-O\" notation is less precise in describing behavior of a sequence or function than the \"little-o\" notation.