For the following questions, choose the correct answers from the codes (a), (b), (c) and (d) def...

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For the following questions, choose the correct answers from the codes (a), (b), (c) and (d) defined as follows.
(a) Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I
(b) Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I
(c) Statement I is true, Statement II is false
(d) Statement I is false, Statement II is true
Statement I If \( f(x)=[x](\sin x+\cos x-1) \)
(where [ [ ] denotes the greatest integer function),
then \( f^{\prime}(x)=[x](\cos x-\sin x) \) for any \( x \in \) integer.
Statement II \( f^{\prime}(x) \) does not exist for any \( x \in \) integer.
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