In this question, $k$ is a positive integer.
Consider the following theorem:
If $2 ^ { k } + 1$ is a prime, then $k$ is a power of $2 . \quad ( * )$
Which of the following statements, taken individually, is/are equivalent to (*)?
I If $k$ is a power of 2 , then $2 ^ { k } + 1$ is prime.
II $\quad 2 ^ { k } + 1$ is not prime only if $k$ is not a power of 2 .
III A sufficient condition for $k$ to be a power of 2 is that $2 ^ { k } + 1$ is prime.

\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
 & Statement I is equivalent to (*) & Statement II is equivalent to (*) & Statement III is equivalent to (*) \\
\hline
A & Yes & Yes & Yes \\
\hline
B & Yes & Yes & No \\
\hline
C & Yes & No & Yes \\
\hline
D & Yes & No & No \\
\hline
E & No & Yes & Yes \\
\hline
F & No & Yes & No \\
\hline
G & No & No & Yes \\
\hline
H & No & No & No \\
\hline
\end{tabular}
\end{center}