Let $x$, $y$, and $z$ be integers such that
\begin{itemize}
\item The product $x \cdot y$ is an even number
\item The sum $x + z$ is an odd number
\item The sum $y + z$ is an odd number
\end{itemize}
Given this;\\
I. $x$ is an odd number.\\
II. $y$ is an even number.\\
III. $z$ is an odd number.\\
Which of these statements are true?\\
A) Only I\\
B) Only III\\
C) I and II\\
D) II and III\\
E) I, II and III