Which of the following describes the largest subset of values of y within the closed interval [0, \pi] for which
\sin (x+y) \leq \sin (x)+\sin (y)
for every x between 0 and \pi, inclusive?
Answer Choices
A. y=0
B. 0 \leq y \leq \dfrac{\pi}{4}
C. 0 \leq y \leq \dfrac{\pi}{2}
D. 0 \leq y \leq \dfrac{3 \pi}{4}
E. 0 \leq y \leq \pi