For positive functions $f(n)$ and $g(n)$ on $\mathbb{N}$. If $f(n) = O(g(n))$ and $f(n) = \Omega(1)$, how many of the following statements are true?

• $g(n) = \Omega(f(n))$
• $f(n) \cdot \log(1+f(n)) = O(g(n) \cdot \log(1+g(n)))$
• $2^{f(n)} = O(2^{g(n)})$
• $(f(n))^k = O((g(n))^k)$ for any $0 < k < 1$