If \( p \) is a prime number, which of the following must be true?

\(\begin{array}{r r l}
&\text{I.} & p\ \text{is odd.}\\

&\text{II.} & p\ \text{is not divisible by}\ 6.\\

&\text{III.} & p\ \text{is not divisible by}\ 7.\\

\end{array}\)

(A)\(\ \ \) I only

(B)\(\ \ \) II only

(C)\(\ \ \) I and II only

(D)\(\ \ \) I and III only

(E)\(\ \ \) II and III only

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