Consider the following statements:
I. \( \quad f:[0,2 \pi] \rightarrow[-1,1] \) defined by \( f(x)=\sin x \) is
\( \mathrm{P} \)
many-one and onto
W
II. \( \quad f:\left[0, \frac{\pi}{2}\right] \rightarrow[-1,1] \) defined by \( f(x)=\sin x \) is one-one and into
III. \( f:[0, \pi] \rightarrow[-1,1] \) defined by \( f(x)=\sin x \) is many-one and into
IV. \( f:\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \rightarrow[-1,1] \) defined by \( f(x)=\sin x \) is bijective function
Which of the above statements is/are correct?
(1) I and II only
(2) I, II and IV only
(3) II, III and IV only
(4) All are correct
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