Comprehension
: Consider the two equations in \( x \)
(i) \( \sin \left(\frac{\cos ^{-1} x}{y}\right)=1 \)
(ii) \( \cos \left(\frac{\sin ^{-1} x}{y}\right)=0 \)
The sets \( X_{1}, X_{2} \in[-1,1] ; Y_{1}, Y_{2} \in I-\{0\} \) are such that
\( X_{1} \) : the solution set of equation (i)
\( X_{2} \) : the solution set of equation (ii)
\( Y_{1} \) : the set of all integral values of \( y \) for which equation
(i) possess a solution
\( Y_{2} \) : the set of all integral values of \( y \) for which equation
(ii) possess a solution
Let \( C_{1} \) be relation defined by \( x C_{1} y \) for \( x \in X_{1}, y \in Y_{1} \) and \( (x, y) \) satisfy (i).
Let \( C_{2} \) be relation defined by \( x C_{2} y \) for \( x \in X_{2}, y \in Y_{2} \) and \( (x, y) \) satisfy (ii).
On the basis of above information, answer the following questions:
\( C_{1}: X_{1} \rightarrow Y_{1} \) is a function which is
(a) One-one
(b) Many-one
(c) Onto
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