$$\begin{array} { l l }
p : & x = 0 \\
q : & y = 0
\end{array}$$
The following propositions are given.
Accordingly, for real numbers x and y
I. $x \cdot y = 0$
II. $x + y = 0$
III. $x ^ { 2 } + y ^ { 2 } = 0$
Which of the following propositions are equivalent to the proposition $\mathbf { p } \wedge \mathbf { q }$?
A) Only II
B) Only III
C) I and II
D) I and III
E) II and III