Consider two statements below -
- $\text{S1}:$ For all positive $f(n), f(n) + o(f(n)) = \theta(f(n)).$
- $\text{S2}:$ For all positive $f(n), g(n)$ and $h(n),$ if $f(n) = O(g(n))$ and $f(n) = \Omega(h(n)),$ then $g(n) + h(n) = \Omega(f(n))$
Which of the following is the correct option.
- $\text{S1}$ is True but $\text{S2}$ is False.
- $\text{S2}$ is True but $\text{S1}$ is False.
- Both are True.
- Both are False.